T02/024 : ELECTROMAGNETIC RADIATION AND HYDROGEN LINE SPECTRUM Flashcards
What do quantum numbers describe?
- energy of e in an orbit
- position of e from nucleus
- shape and number of orbitals around its own axis
- orientation of the spinning of the electron round its own axis
MAPS
What are the four types of quantum number?
- principal quantum numer (n)
- azumuthal quantum number (l)
- magnetic quantum number(m)
- spin quantum number(s)
energy level, distance, energy,
What properties of an electron does the principal quantum number reveal?Explain using formulas.
- rep. main energy level i which the electron revolves round the nucleus e.g n=1,2,3,
- gives distance of e from nucleus(radius of the orbit) e.g
r = (E’oh^2n^2)/(πme^2 Z) - gives energy of an e in an orbit
E = -(me^4Z^2)/(8E’^2h^2n^2) - gives maximum number of e that can be accomodated in a given shell
= 2n^2
E’ is permittivity
sub-shell, max. e , angular
What properties of an electron does the azimuthal quantum number(l) reveal?
- rep a sub-shell within the principal sub-shell i.e
l=0 …………… s-sub-shell (s-orbital)
(s-sharp)
l=1…………… p-sub-shell (p-orbital)
(p-principal)
l=2 …………… d-sub-shell (d-orbital)
(d-diffused)
l=3 …………… f-sub-shell (f-orbital)
(f-fundamental) - determines the magnitude of orbital angular momentum
- explains the group of closely spaced lines in the hydrogen spectrum
- maximum number of e in a sub shell i.e
2(2l+1)
sharp, diffused, fundamental and principal
Describe the sub-shells defined by azimuthal quantum number.
The azimuthal quantum number (denoted as ℓ) defines the subshells or orbital angular momentum in an atom. It determines the shape of the electron’s orbital and its energy in a given shell (principal quantum number, n). For each value of n, the azimuthal quantum number ℓ can take integer values from 0 to n-1, and each value of ℓ corresponds to a specific type of subshell:
- ℓ = 0: This defines the s subshell (sharp). The orbital is spherical in shape. Each s subshell can hold a maximum of 2 electrons.
- ℓ = 1: This defines the p subshell (principal). The orbitals are dumbbell-shaped and oriented along the x, y, and z axes. A p subshell has three orbitals and can hold a maximum of 6 electrons.
- ℓ = 2: This defines the d subshell (diffuse). The orbitals have more complex shapes, often described as clover-shaped. A d subshell has five orbitals and can hold a maximum of 10 electrons.
- ℓ = 3: This defines the f subshell (fundamental). The orbitals are even more complex in shape. An f subshell has seven orbitals and can hold a maximum of 14 electrons.
- ℓ = 4 and higher: These correspond to g, h, i subshells, though they are not typically encountered in most ground-state atoms. Each follows the same rule, with increasing complexity in orbital shapes and a maximum number of electrons increasing by 4 per higher subshell (e.g., g can hold 18 electrons).
In summary, the azimuthal quantum number defines the number and type of subshells within a given shell, influencing the shape of the electron cloud and the total number of electrons that the subshell can accommodate.
(i)What is the number of sub-shells when the principal quantum number is n=5?
(ii)What are the type of sub-shells included?
(iii)What is the maximum number of e in each subshell?
(i) Number of sub-shells when n = 5:
The number of subshells is determined by the principal quantum number (n). For each value of n, the azimuthal quantum number ℓ can take integer values from 0 to n-1. So, when n = 5, the possible values of ℓ are:
- ℓ = 0 (s subshell)
- ℓ = 1 (p subshell)
- ℓ = 2 (d subshell)
- ℓ = 3 (f subshell)
- ℓ = 4 (g subshell)
Therefore, there are 5 subshells when n = 5.
(ii) Type of subshells included:
The types of subshells correspond to the values of ℓ:
- ℓ = 0 → 5s subshell
- ℓ = 1 → 5p subshell
- ℓ = 2 → 5d subshell
- ℓ = 3 → 5f subshell
- ℓ = 4 → 5g subshell
So, the subshells included are 5s, 5p, 5d, 5f, and 5g.
(iii) Maximum number of electrons in each subshell:
The maximum number of electrons in each subshell is given by the formula 2(2ℓ + 1), where ℓ is the azimuthal quantum number.
- 5s (ℓ = 0): Maximum electrons = 2(2(0) + 1) = 2 electrons
- 5p (ℓ = 1): Maximum electrons = 2(2(1) + 1) = 6 electrons
- 5d (ℓ = 2): Maximum electrons = 2(2(2) + 1) = 10 electrons
- 5f (ℓ = 3): Maximum electrons = 2(2(3) + 1) = 14 electrons
- 5g (ℓ = 4): Maximum electrons = 2(2(4) + 1) = 18 electrons
In summary:
- 5s can hold 2 electrons.
- 5p can hold 6 electrons.
- 5d can hold 10 electrons.
- 5f can hold 14 electrons.
- 5g can hold 18 electrons.
addition due to magnetic field, orbital orientations
What does the magnetic quantum number show?
- explains the additional number of spectral lines when the magnatic field is pplied.
- total number of orbital orientations in a given sub-shell
- takes values from -1, 0, +1
- l = 0; m = 0
l = 1; m = -1, 0, +1
l = 2; m = -2, -1, 0, +1, +2
l = 3; m = -3, -2, -1; 0; +1; +2; +3
up,down
Explain the spin quantum number and the different representations of an electron spin
The spin quantum number (denoted as ms) refers to the intrinsic angular momentum or spin of the electron.
Representation of electron spinning:
1)Clockwise (+ ½ ) or ( arrow pointing up) or (α spin)
2)Anticlockwise (- ½) or (arrow pointing down ) or (β spin)
Distinguish the type of atomic orbitals
Atomic orbitals are regions around the nucleus of an atom where there is a high probability of finding electrons. Each orbital is defined by a unique set of quantum numbers that describe its shape, size, and orientation. The four main types of atomic orbitals are s, p, d, and f, each having distinct shapes and capacities for holding electrons.
- s Orbitals:
Shape: Spherical.
Principal Quantum Number (n): Present in all energy levels (n = 1, 2, 3,…).
Azimuthal Quantum Number (ℓ): ℓ = 0.
Number of Orbitals: 1 s orbital per energy level.
Maximum Electrons: Can hold up to 2 electrons.
The size of the s orbital increases with increasing n, meaning that 1s is smaller than 2s, 2s is smaller than 3s, and so on.
- p Orbitals:
Shape: egg-shaped lobes
Principal Quantum Number (n): Present starting from the second energy level (n = 2, 3, 4,…).
Azimuthal Quantum Number (ℓ): ℓ = 1.
Number of Orbitals: 3 p orbitals (denoted as px, py, and pz) in each energy level starting from n = 2.
Maximum Electrons: Each p orbital can hold 2 electrons, so the total for all three p orbitals is 6 electrons.
The p orbitals are oriented along the three Cartesian axes (x, y, and z) and have a node at the nucleus.
- d Orbitals:
Shape: More complex; four of the five d orbitals have cloverleaf shapes, and one (dz²) is shaped like a doughnut with a ring around the center.
Principal Quantum Number (n): Present starting from the third energy level (n = 3, 4, 5,…).
Azimuthal Quantum Number (ℓ): ℓ = 2.
Number of Orbitals: 5 d orbitals (denoted as dxy, dyz, dxz, dx²-y², and dz²).
Maximum Electrons: Each d orbital can hold 2 electrons, so the total for all five d orbitals is 10 electrons.
d orbitals become important for transition metals, and they play a key role in bonding and magnetic properties.
- f Orbitals:
Shape: Even more complex than d orbitals, with intricate, multilobed shapes.
Principal Quantum Number (n): Present starting from the fourth energy level (n = 4, 5, 6,…).
Azimuthal Quantum Number (ℓ): ℓ = 3.
Number of Orbitals: 7 f orbitals.
Maximum Electrons: Each f orbital can hold 2 electrons, so the total for all seven f orbitals is 14 electrons.
f orbitals are significant for the chemistry of the lanthanides and actinides (rare earth elements).
Key Differences Between the Types of Orbitals:
Orbital Azimuthal Shape Number Maximum First Energy
Quantum of Electrons Level Number (ℓ) Orbitals Present
s 0 Spherical 1 2 n = 1
p 1 Dumbbell 3 6 n = 2
d 2 Cloverleaf 5 10 n = 3
f 3 Complex lobes 7 14 n = 4
Visual Representation:
s Orbital: Simple sphere around the nucleus.
p Orbital: Two lobes extending from either side of the nucleus (along the x, y, or z axis).
d Orbital: Four-lobed cloverleaf structures, except for the dz² orbital, which has a doughnut-like ring.
f Orbital: Complex multilobed shapes with no simple geometry.
Importance of Orbitals:
s Orbitals: Found in every atom and important for forming sigma bonds.
p Orbitals: Essential for forming pi bonds in molecules and contributing to molecular geometry.
d Orbitals: Critical in transition metal chemistry, complex ion formation, and magnetic properties.
f Orbitals: Important in lanthanides and actinides, affecting their unique properties and behavior in complex compounds.
Each type of orbital plays a significant role in the chemical bonding, structure, and properties of elements and compounds.
Describe the s-orbital
- accomodate max. of 2 e
- sypherically symmetrical in shape, non-directional and occur
What is a radial node?
a node is a region in space where the probability of finding an e is zero
3, egg
Describe p-orbitals
- occurs when l=1; m= -1, 0, +1; n>=2
- 3 p-orbitals
- each has 2 egg-shaped lobes on each side of the nucleus
- probability of finding e in each lobe is the same e.g degenrate orbitals (same energy level)
- Both lobes are separated by nodal plane which passes through the nucleus.
- The electron density on the plane and the nucleus is zero.
MUST DRAW!!
Draw/distinguish s and p orbitals
- draw lobes of p-orbitals and each corner of egg should be on -ve and +ve sides.
- each of the p-orbitals have 2 have 2 lobes ; eggs
- p-orbitals are on x,y,z axes.
- s orbitals look like circle on axis
Describe d-orbitals
- occurs when n>=3; l=2; m=-2,-1,0,1,2
- are dumbell shaped
- all 5 orbitals are degenerate
- Three of the d-orbitals lie in a plane bisecting the x-, y- and z-axes, the
remaining two lie in a plane aligned along the x-, y- and z-axes. - Four of the d-orbitals have four lobes each, but one has two lobes and a
collar.
lobes = eggs
Draw d-orbitals
- the orbitals :
- dxy, dxz, dyz - lobes(4) are not directly on axes but between axes mentioned i.e dxy, lobes are between x and y axes and one lobe in z axis.
- dx^2-dy^2 - 4 lobes are on x and y axes
- dz^2 - 2 lobes on z axis + a collar
Describe f-orbital shapes
- occur when n>= 4; l=3; m=-3,-2,-1,0,1,2,3
- 7 types of f-orbitals
- …
- ## take 14 e
State Pauli Exclusion Principle
no electrons in the same atom have the same 4 quantum nubers (n,l,m,ms).It follows that each orbital can occupy a maximum of 2 e with different ms values
Describe Aufbau Principle(building up principle)
each added e occupies a higher energy sub-shells only after the lower energy sub-shells are fully filled.
Describe Hund’s rule
single e with the same spin occupy an equal-energy orbital before additional electrons of opposite spins occupy the same orbital
eg if the electrons are 8 (4 go to s orbitals 2 pairs in different spins), the last 4 go to p-orbitals in one direction of spin
probability, wave function, forces,positions and velocities
Differentiate the definition of a sytem based on classical mechanics and quantum mechanics
- in classical mechanics, a system is defined by specifying all the forces acting on it, the positions and the velocities.
- quantum mechanics defines a system by the wave function.
- knowledge of q.m invloves probabilities rather than certainties.
Derive de Broglie’s wavelength equation
- De Broglie’s theory assumed that all small particles like e, protons, neutrons and atoms when in motion posses wave properties like wavelengh, amplitude and frequency.
wavelength = h/mc = h/mv
From Einstein’s equation, E = cp
From Planck’s constant, E = hv
… E = hc/wavelength
E/c= h/wavelength
p = h/wavelength
From Planck’s equation, E=hv
From Einstein’s equation, E=mc^2
mc^2 = hv = hc/wavelength
mc^2=hc/wavelength
mc=h/wavelength
wavelength = h/mc
wavelength = h/mc=h/mv
Describe Heisenberg uncertainity principle
- Heisenberg proposed that it is impossible to accurately determine the position and momentum of a very small particle simultaneously.If one was to observe a smnall particle like an electron, they’d have to irradiate it with light.The collision between the photon and the particle causes a change in the position and the momentum of the particle.
What is Heisenberg’s expression?
Δx * Δp >= h/4π
or
Δx * Δmv >= h/4π
Derive Schrodinger wave function
What are the conclusions/implications of De Broglie’s equation?
- everything in nature exhibits wave and particle properties.
- large objects mostly show particle-like behavior.
- small objects exhibit wave particles mostly.
Differentiate between a shell and sub-shell
A shell and a sub-shell are terms used in atomic structure to describe the arrangement of electrons around the nucleus of an atom. Here’s how they differ:
Shell:
- A shell refers to the main energy level of an atom and is denoted by the principal quantum number, ( n ) (e.g., ( n = 1, 2, 3, ) etc.).
- It represents the general region where electrons are likely to be found at a certain distance from the nucleus.
- Shells are labeled as ( K, L, M, N ), corresponding to ( n = 1, 2, 3, 4, ) respectively.
- Example: The first shell (( n = 1 )) is closest to the nucleus and has the lowest energy.
Sub-shell:
- A sub-shell refers to a subdivision of a shell and is defined by the azimuthal quantum number, ( l ), which determines the shape of the orbital within a shell.
- Sub-shells are labeled as ( s, p, d, f, ) corresponding to ( l = 0, 1, 2, 3 ), respectively.
- Each shell can contain one or more sub-shells depending on the value of ( n ).
- For example:
- ( n = 1 ) has one sub-shell: ( 1s ).
- ( n = 2 ) has two sub-shells: ( 2s ) and ( 2p ).
- ( n = 3 ) has three sub-shells: ( 3s, 3p, ) and ( 3d ).
Key Difference:
- Shell defines the energy level of an electron, while sub-shell specifies the type and shape of the orbital within that energy level.
Summary:
- Shell: Broad region defined by ( n ), e.g., ( n = 2 ) (L-shell).
- Sub-shell: Subdivision within a shell defined by ( l ), e.g., ( 2s, 2p ).
The energy of orbital is determined by the n+l rule.Define the rule?
1) Orbital having lower value of n+l will have lower energy e.g. 2s< 2p.
2) Orbitals having similar (n+l) values, the orbital with lower value of n
will have lower energy eg. 3p<4s.
List 2 methods of identifying elements
- flame test
- spectroscopy
emr,matter
Define :
1. Spectroscopy
2. Spectroscope
1.The study of interaction between emr and matter
2.A device used to study the group of wavelengths of light given off by an element
energy,electric and magnetic field?propagation?
what is electromagnetic radiation?
This is a stream of energy moving in the direction of propagation and perpendicular to electric and magnetic field.
What are the properties of electromagnetic radiation?
- do not require a medium to travel
- travel with the velocity of light, c
- have dual nature - exhibit particle and wave-like properties
- it has electric and magnetic components that travel perpendicular to each other and perpendicular to the direction of propagation.
Define(giving their SI units and symbols):
1.Wavelength
2.Frequency
3.Wave number
4.Velocity
- Wavelength (symbol = λ pronounced as “lambda”)(m)
- distance between two consecutive peaks in a wave.
2.Frequency(symbol = ν , pronounced as “nu”)(Hz =1/s)
- number of waves/cycles passing through a point on the x-axis per second.
- velocity (symbol = c)(m/s)
- velocity of light = 3 x 10^8 m/s
C = λ ν ……………………….Eq. 1
λ = c/ ν and ν = c/ λ …..Eq. 2
4.wave number(symbol ν , pronounced as nu bar)(m^-1)
- the reciproval of wavelength
ν = 1/ λ = ν/c ………………………..Eq. 3
What are the different types of emr?
1.Gamma rays
2.X-rays
3.UV Rays
4.Visible Light
5.Infrared rays
6.Microwaves
7.Radio waves
What are the different types of atomic and molecular transitions of emr?
1.Gamma rays - nuclear
2.X-rays - core-level electrons
3.UV Rays - valence electrons
4.Visible Light - valence electrons
5.Infrared rays - molecular vibrations
6.Microwaves - molecular rotations ; electron spin
7.Radio waves - nuclear spin
The interaction of electromagnetic radiation (EMR) with atoms and molecules causes transitions between different energy levels. These atomic and molecular transitions are classified based on the nature of the energy levels involved. Below are the main types of transitions:
1. Electronic Transitions
- What Happens: Electrons in an atom or molecule move between different electronic energy levels.
- Energy Requirement: High energy, typically in the UV or visible region.
- Examples:
- Absorption or emission of light in hydrogen atoms (Lyman, Balmer series).
- Excitation of electrons in pigments causing color.
2. Vibrational Transitions
- What Happens: Molecules change their vibrational energy state, often within the same electronic energy level.
- Energy Requirement: Moderate energy, typically in the infrared (IR) region.
- Examples:
- Infrared absorption spectroscopy (e.g., CO(_2) or H(_2)O detecting IR radiation).
- Molecules stretching and bending.
3. Rotational Transitions
- What Happens: Molecules transition between different rotational energy levels.
- Energy Requirement: Low energy, typically in the microwave region.
- Examples:
- Rotational spectroscopy in gases (e.g., water vapor, ammonia).
4. Spin Transitions
- What Happens: Changes in the orientation of particle spins (electrons, nuclei) relative to a magnetic field.
- Energy Requirement: Very low energy, typically in the radiofrequency region.
- Examples:
- Nuclear Magnetic Resonance (NMR) spectroscopy.
- Electron Spin Resonance (ESR) spectroscopy.
5. Ionization Transitions
- What Happens: An electron gains enough energy to escape the atom or molecule completely, leading to ionization.
- Energy Requirement: Very high energy, typically in the X-ray or UV region.
- Examples:
- Photoionization in X-ray absorption.
- Ionization of gases in electric discharges.
6. Molecular Orbital Transitions
- What Happens: Electrons transition between molecular orbitals, such as (\pi \rightarrow \pi^) or (n \rightarrow \pi^).
- Energy Requirement: Typically in the UV or visible region.
- Examples:
- UV-Visible spectroscopy used to analyze conjugated systems in organic molecules.
7. Inner-Shell Electronic Transitions
- What Happens: Electrons from inner shells (e.g., (K)-shell) are excited to higher energy levels.
- Energy Requirement: High energy, typically in the X-ray region.
- Examples:
- X-ray fluorescence (XRF) spectroscopy.
- Auger electron emission.
These transitions provide the basis for various spectroscopic techniques, each targeting specific energy levels to analyze the structure, composition, and dynamics of atoms and molecules.
What is an electromagnetic radiation spectrum?
- it is the entire range of electromagnetic radiations separated into different frequencies and wavelengths
briefly describe the properties of emr and their application
Properties of Electromagnetic Radiation and Applications
1. Rotational, Vibrational, and Electronic Spectroscopy
- Key Interaction:
- In these types of spectroscopy, the electric field component of electromagnetic radiation interacts with the molecular system.
- This interaction can induce changes in rotational, vibrational, or electronic energy levels of the molecule.
- Mechanism:
- The molecule absorbs radiation when the energy of the radiation matches the energy difference between two allowed energy levels.
- The absorption results in molecular transitions, such as:
- Rotational transitions in the microwave region.
- Vibrational transitions in the infrared (IR) region.
- Electronic transitions in the visible and ultraviolet (UV) regions.
- Applications:
- Rotational Spectroscopy: Identifies molecular structure and bond lengths.
- Vibrational Spectroscopy (e.g., IR spectroscopy): Determines functional groups in organic compounds.
- Electronic Spectroscopy (e.g., UV-Vis): Studies conjugated systems, molecular orbitals, and color in substances.
2. Electron Paramagnetic Resonance (EPR) and Nuclear Magnetic Resonance (NMR) Spectroscopy
- Key Interaction:
- In these techniques, the focus is on the magnetic field component of electromagnetic radiation interacting with magnetic properties of particles (electrons or nuclei).
- This is distinct from rotational, vibrational, and electronic spectroscopy, which rely on electric field interactions.
- Mechanism:
- EPR: Studies unpaired electron spins. A magnetic field aligns the electron spins, and microwave radiation causes transitions between spin states.
- NMR: Examines nuclei with a magnetic moment (like ( ^1H ) or ( ^13C )). A strong external magnetic field causes nuclei to align, and radiofrequency radiation induces transitions between nuclear spin states.
- Applications:
- EPR Spectroscopy:
- Analysis of free radicals and transition metal complexes.
- Studies of paramagnetic species in biological and chemical systems.
- NMR Spectroscopy:
- Structural determination of organic compounds and biomolecules.
- Quantitative analysis and studying molecular dynamics in chemistry and medicine (e.g., MRI imaging in clinical diagnostics).
Summary of Key Differences
- Electric Field Interaction: Used in rotational, vibrational, and electronic spectroscopy to induce transitions based on energy differences between molecular levels.
- Magnetic Field Interaction: Used in EPR and NMR spectroscopy to study spin dynamics and magnetic properties of particles.
Both approaches provide complementary insights into molecular and atomic systems.
Give some properties of light as emr
Light is electromagnetic radiation and is described as either particles,
called photons, with discrete amount of energy or as waves with electric
and magnetic fields perpendicular to each other and to the direction of
propagation.
- The particulate nature of light explains the interactions of light with matter
that leads to absorption and emission of energy.
* The wave when light interacts with materials it undergo refraction, diffraction, and
reflection.
* Reflection occurs when light bounces off a surface.
* Refraction is the bending of light when it travels from one media to another.
* Diffraction is the spreading of light when it passes through a narrow opening
or around an object.
* Based on the wavelike nature of electromagnetic radiation, light can be described in
terms of its wavelength and frequency.
* The wavelike nature of light can be characterized by energy of the photons (E)
traveling in the electromagnetic field and their wavelength (λ) or frequency (ν)
through the following equation:
* E = hv = hc/λ or λ =hc/ΔE
Distinguish emission and absorption spectra
**Property** | **Emission Spectrum** | **Absorption Spectrum** | **Definition** | The spectrum of light emitted by atoms or molecules when electrons transition from higher to lower energy levels. | The spectrum showing dark lines or bands where light is absorbed as electrons transition from lower to higher energy levels. | | **Cause** | Caused by the release of energy as electrons return to lower energy states. | Caused by the absorption of energy as electrons move to higher energy states. | | **Appearance** | Bright lines or bands on a dark background. | Dark lines or bands on a continuous spectrum (rainbow background). | | **Energy Transition** | Energy is **released** by the atom or molecule. | Energy is **absorbed** by the atom or molecule. | | **Observation** | Observed when a substance is excited (e.g., by heat or electricity) and emits radiation. | Observed when white light passes through a substance, and specific wavelengths are absorbed. | | **Examples** | - Flame tests (e.g., sodium produces yellow emission).<br>- Neon signs.<br>- Astronomical observations (stars). | - Photosynthesis (chlorophyll absorbs specific wavelengths).<br>- Atmospheric studies (absorption of sunlight by gases). | | **Instrumentation** | Emission spectrometer. | Absorption spectrometer (e.g., UV-Vis, IR spectrometer). | | **Spectrum Type** | **Line spectrum** for atoms and **band spectrum** for molecules. | **Dark-line spectrum** superimposed on a continuous spectrum. | | **Applications** | - Identifying elements in stars or flames.<br>- Study of excited states of atoms. | - Determining the composition of gases.<br>- Analyzing solutions or materials (e.g., UV-Vis spectroscopy). |
what is planck’s theory of radiation?
This theory explains that energy is absorbed or emitted not continuously, but in discrete packets called quanta, which are proportional to the frequency of the radiation and occur in whole-number multiples.
How do you use the theory to calculate wavelength, energy, frequency of emr?
E = hv = hc/λ
What are the different types of spectra and how are they produced?
- absorption
- emission
Define a spectrum and diffraction
Separation of a composite radiation into different wavelengths or frequencies.
Diffraction is a process by which a beam of light or other sytem of waves is spread out as a result of passing through a narrow aperture
How do you use emr to identify elements using the spectra?
Each element has a unique electronic structure, leading to a unique set of energy levels.
The interaction of EMR with these energy levels produces distinct spectral patterns, acting as a “fingerprint” for the element.
Just read through
What are the different types of absorption and emission spectrum?
1) Absorption spectrum
* Absorption spectrum is produced when light from a source that emits a
continuous range of wavelengths is passed through a substance (solid,
liquid or gas) at lower temperature and observed through a spectrometer.
* The substance absorbs some of the wavelengths leaving dark lines (or dark
bands or continuous dark region) at their places
Depending on the type of substance absorbing the radiation, the
spectrum can be:
i) Continuous absorption spectrum
Occurs when a continuous range of wavelengths are absorbed by the
sample producing continuous dark regions e.g. When the glass absorbs
all wavelengths except red.
ii) Band absorption spectrum
It consists of dark bands produced in absorption spectrum of aqueous
solution e.g. KMnO4 gives five dark absorption bands.
iii) Line absorption spectrum
It consists of discrete dark lines produced when absorbing materials are in
vapour or gaseous phase.
2) Emission spectrum
* Emission spectrum is produced by heating a substance directly in a flame
or electrically and passing the emitted radiation through a prism or a
grating.
* The spectrum produced is characteristic for each element, hence can be
used to identify the element.
i) Continuous emission spectrum
It consists of a wide band of continuous wavelengths which appear as
continuous band of light.
It is produced by incandescent solids e.g. Hot filament , hot iron etc.
The intensity of spectrum is not uniform over the entire range i.e. is
maximum at particular wavelengths
ii) Band emission spectrum
It consists of luminous bands separated by dark
spaces.
It is produced by substances in molecular state.
At high resolution, each band is observed to be
comprised of very fine lines.
Examples:
A) vacuum tubes (in electronics, a vacuum tube or
electron tube is a device that controls electric
current between electrodes in an evacuated
container).
B) Carbon arc with metallic salt in its core.
* Electric arc between two carbon electrodes, used for lighting,
as in an arc light for a motion-picture projector; intense
heating for cutting and welding of metals.
iii) Line or atomic emission spectrum
It consists of discrete/separate bright lines produced by gases or vapours of a substance in
atomic state.
The lines are regularly spaced but differ in their intensities.
Examples:
a) hydrogen line spectrum
b) sodium vapour spectrum
c) mercury vapour spectrum
Illustration:
* Hydrogen line
spectrum
What is photoelectric effect and how does it confirm quantization of energy
photoelectric effect is the phenomenon which occurs when a metal surface is photo-irradiated with energy whose frequency is sufficient to overcome the work function of the metal.
Describe the Experimental Setup for Observing the Photoelectric Effect
Illustrate the experimental setup used to observe the photoelectric effect and explain how it demonstrates the emission of electrons.
- A typical setup consists of a metal plate (emitter), positively charged anode, light source, ammeter and Voltage Source: The emitter plate is connected to the negative terminal of a variable direct current (DC) voltage source, while the anode is connected to the positive terminal.
Process:
- When light of sufficient energy strikes the emitter, the photons are absorbed by the electrons in the metal. If the energy of the incident photons (given by the equation E = hf) exceeds the work function (φ), the electrons gain enough energy to break free from the metal’s surface.
Once ejected, the* electrons are attracted to the positively charged anode due to the electric field created by the voltage source. This movement of electrons constitutes an electric current.*
The current can be measured on the meter connected to the circuit, indicating the occurrence of the photoelectric effect. The intensity of the current is directly proportional to the number of electrons emitted, which depends on the intensity and frequency of the incident light.
If the frequency of the incident light is below the cutoff frequency (ν₀), no electrons are emitted, and thus, no current is recorded, regardless of the intensity of the light. This phenomenon illustrates that the photoelectric effect is a quantum mechanical process, supporting the concept of energy quantization.
Analyze the relationship between the frequency of incident light, the kinetic energy of emitted electrons, and the concept of stopping potential.
Answer: The frequency of the incident light must exceed a certain threshold frequency (ν₀) to emit electrons. For frequencies above ν₀, the kinetic energy (KE) of emitted electrons increases, expressed as:
KE=hf−φ
The stopping potential (V_s) is the voltage needed to prevent emitted electrons from reaching the anode, satisfying the equation:
hf−φ=qV
where V = stopping voltage, where q is the charge of the electron.
The stopping potential is independent of the light’s intensity but depends on its frequency.
- In order to make it across the gap, the initial KE of the ejected electron must be greater than the PE at the collector.
- When the voltage equals the stopping potential, we know that the KE for the ejected electrons just equals the potential energy at the collector.
- KE = PE
- hf - ɸ = qV.
This equation is very useful in finding the stopping potential with - V = (hf - ɸ) /q
What is the cutoff frequency in the context of the photoelectric effect, and what implications does it have on the emission of electrons?
The cutoff frequency (ν₀) is the minimum frequency required to emit electrons from a metal surface. Photons with frequencies below this threshold do not possess enough energy to overcome the work function, regardless of intensity. Consequently, no current is observed in the circuit for frequencies below ν₀, demonstrating that light’s wave properties alone do not account for electron emission.
How does Planck’s constant relate to the photoelectric effect, and how can it be determined experimentally?
Planck’s constant (h) is fundamental in quantifying the energy of photons and is represented in the equation:
E=hf
In a graph of kinetic energy (KE) of emitted electrons versus frequency (f) of incident light, the slope of the line yields Planck’s constant. The x-intercept indicates the cutoff frequency, and the y-intercept provides the work function of the metal. This relationship confirms the quantization of energy in light.
Since KEmax = hf - ɸ and KEmax = 0 at fc,
* fc = ɸ/h
Explain how the wavelength of light influences the occurrence of the photoelectric effect and its implications on electron emission.
The relationship between the wavelength of light (λ) and the photoelectric effect is fundamentally linked to the energy of photons and the ability to eject electrons from a metal surface. The key points are:
Photon Energy and Wavelength: The energy (E) of a photon is inversely proportional to its wavelength, as described by the equation:
E = hc/λ
where h = Planck’s constant(6.626 x 10^-34Js), c = 3 x 10^8m/s
and λ is the wavelength of the incident light. As the wavelength increases, the energy of the photons decreases.
Threshold Wavelength: For the photoelectric effect to occur, the energy of the incident photons must exceed the work function (φ) of the metal. This establishes a threshold wavelength (λ₀), below which photoelectrons are emitted. The threshold wavelength is given by:
λ = hc/ɸ
If the wavelength of the incident light is greater than λ₀, photons lack sufficient energy to liberate electrons from the metal surface, resulting in no emission.
Current and Wavelength: In an experimental setup, when the wavelength of light is varied while keeping its intensity constant, current (i) is only observed for wavelengths less than λ₀. For wavelengths longer than this threshold, regardless of the light’s intensity, no current flows, indicating that the photons do not have enough energy to dislodge electrons.
Energy Distribution: For wavelengths that do cause the photoelectric effect (shorter than λ₀), increasing intensity leads to a higher current, as more photons interact with electrons. Additionally, for photons with energies above the threshold, the excess energy is converted into kinetic energy (KE) of the emitted electrons, impacting their velocity.
Graphical Representation: A graph of current versus wavelength reveals a sharp cutoff at λ₀. This emphasizes that only photons with energies above a certain threshold (corresponding to wavelengths shorter than λ₀) contribute to the photoelectric effect, supporting the quantized nature of light.
What factors do classical physics fail to explain?
1) No electrons are emitted if the light frequency falls below fc.
2) Maximum KE doesn’t depend on intensity.
3) Electrons are ejected almost instantaneously
4) KE increases with increasing frequency
How do you calculate KE of e, Planck’s constant(h), Stopping Potential and Work function of metals?
KE = hf - ɸ
h=E/f
V= (hf - ɸ)/q
ɸ = hv = hc/λ
(threshold frequency/wavelength)
Metals and their eV
Metal φ (eV) Sodium 2.28 Zinc 4.31 Cobalt 3.90 Silver 4.73 Platinum 6.35
What is the electronic configuration of phosphorous?
Name the three rules that must be folllowed when coming up with the electron configurations of an element.
Write the shorthand electronic configuration of Copper (z = 29) ?
[Ar]4s^1,3d^10
What is the shorthand configuration of Iron?
why is it 3d^6
What is exchange energy?What is the formula used to calculate exchange energy?
Exchange energy is the **energy associated with the parallel spin alignment of electrons in degenerate orbitals **(orbitals of the same energy level) of an atom.
The repulsion between the electrons if they have anti-parallel spins is greater than if they have parallel spins, e.g. for a p2 configuration.
* The difference in energy between opposite spin and parallel spin electron arrangement can be explained by difference in exchange energy K. This accounts for the extra stability attained for parallel spin
configuration.
Exchange Energy (E_exchange) = Σ [N * (N - 1) / 2] * K
Explain exchange energy
Exchange energy is the energy associated with the parallel spin alignment of electrons in degenerate orbitals (orbitals of the same energy level) of an atom. It arises due to the quantum mechanical exchange interaction, which is a result of the indistinguishability and wave nature of electrons.
Explanation:
1. Pauli Exclusion Principle:
- No two electrons in an atom can have the same set of quantum numbers.
- If electrons occupy degenerate orbitals (e.g., ( p, d, ) or ( f ) orbitals), they prefer to have parallel spins to maximize exchange energy.
-
Quantum Mechanical Effect:
- Electrons with parallel spins are less likely to come close to each other because their wavefunctions overlap less.
- This reduces electron-electron repulsion, stabilizing the system.
-
Contribution to Stability:
- The more the parallel spins, the greater the exchange energy and the greater the stability of the atom or ion.
- This principle explains why electrons fill degenerate orbitals singly before pairing up (Hund’s Rule).
Mathematical Representation:
For an atom, the exchange energy (( E_\text{exchange} )) depends on the number of unpaired electrons (( n )):
[
E_\text{exchange} \propto \frac{n(n - 1)}{2}
]
This formula accounts for all possible pairs of unpaired electrons with parallel spins.
Example:
In a ( d^5 ) configuration (e.g., in ( \text{Mn}^{2+} )):
- The ( 5 ) electrons are in ( 5 ) degenerate ( d )-orbitals with parallel spins.
- The exchange energy is maximized, contributing significantly to the stability of the ( d^5 ) configuration.
Significance:
- Stability of Half-Filled and Fully Filled Orbitals:
- Half-filled (( d^5 )) and fully filled (( d^{10} )) sub-shells have high exchange energy, making them exceptionally stable.
- Magnetic Properties:
- The number of unpaired electrons (linked to exchange energy) determines magnetic behavior like paramagnetism.
Define :
1. Outermost shell
2. Inner shells
3. Penultimate shell
4. Antenultimate shell
Outermost shell: is the shell with maximum number of n value that is
fully or partially filled. Also called valence shell, and electrons in this
shell are called valence electrons
* Inner shells: are the shells other than the valence shell. The total
number of electrons in the inner shells are called core electrons or
kernel electrons
* Penultimate shell: this is the shell just before the valence shell i.e. (n-
1)nth shell, where n represents the valence shell.
* Antepenultimate shell: this is the (n-2)nth shell where n refers to the
valence shell
What is :
1.effective nuclear charge/effective atomic number?
2.screening constant
3.the formula to calculate effective nuclear charge
- Effective nuclear charge ; net charge experienced by an electron in a multi-electron atom.
- Screening constant is a measure of how much the inner electrons in an atom reduce the effective nuclear charge felt by an outer electron. It quantifies the shielding effect caused by inner electrons, which partially block the attraction between the nucleus and the outermost electrons.
Zeff = Nuclear Charge (Z) – Screening Constant (σ)
Define the Slates rules
1)Determination
- Calculate the values of σ and Zeff for 4s and 3d electrons in Mn; Cu; Cr
Give 5 characteristics of the s-block elements
- elements in which the last e fills the s-orbital
- are located at the extreme left of the periodic table (Group 1 and 2)
- consist of high electropositive metals
- outer shell is partially filled
- valence shell configuration is ns^(1-2)
Give characteristics of p-block elements
- occur on the extreme right hand of periodic table
- the nth shell of noble gases is completely filled
- The (n-1)th shell of p-block elements of the 3rd period has 8 electrons,
whereas that of the 4th, 5th and 6th periods has 18 electrons - The (n-2)th shell of p-block elements of the 5th has 18 electrons
whereas that of the 6th has 32 (18+14) due to the inclusion of 14
Lanthanides - The 2nd shell of the p-block elements has 3 electrons whereas the 3rd
other periods has 8 electrons. The 1st shell of this block has 2 electrons
Give characteristics of d-block elements
i. They often form coloured compounds
ii. They can have a variety of different oxidation states
iii. They are often good catalysts e.g. Mn, Fe, Co, Cr
iv. They are silvery-blue at room temperature (except copper and gold)
v. They are solids at room temperature (except mercury)
vi. They form complexes
vii. They are often paramagnetic.
give characteristics of f-block elements:
(i)Lanthanides
(ii)Actinides
1) Lanthanides
- Silvery metals.
- High melting points.
- Found mixed in nature and hard to separate.
- Used in:
* Movie projectors; Welder’s goggles
* TV and Computer monitors
2) Actinides
- Radioactive elements.
- Only 3 exist in nature.
- Remaining are synthetic (transuraniumelements) – greater
atomic number than uranium.
- Decay quickly.
- Used in: Home smoke detectors, nuclear power plants.
What is :
(a)Atomic properties
(b)Ionization energy
(c)First ionization energy
Compare the first, second and third IE
- the first ionization energy is lower than 2nd which is lower than 3rd
Why does :
1.ionization and Effective nuclear charge energy decrease down a group
2.ionization and Effective nuclear charge increase across a period
stability in p-orbitals
Explain why magnesium has a higher ionization energy than aluminium
Using the concept of core electrons, explain why
(1)the second ionisation of Sodium is higher than its first.
(2)the second ionisation energy of sodium is higher than magnesium
(2)Sodium is losing a core electron while Magnesium is losing a valence electron
Define :
(1)Bond distance
(2)Covalent radius
(3)Van der Waals radius
(4)Iso-electrons
(5)Electron affinity
(6)Electronegativity
(7)
Why is the atomic radius of metals smaller than non-metals?
Expain the behavior of atomic radii across the period and down the group
Explain the behavior of ionic radii :
(1)across a period
(2)down a group
(3) across metallic elements
(4) across non-metallic elements
E
- the larger the number of protons as compared to e , the smaller the ion
- the larger the number of e , the larger the ion
Explain the behavior of electron affinity…
- the higher the negative value the higher the electron affinity
- the higher the positive value, the lower the e affinity
Describe the scales used in calculating electronegativity:
(a)Pauling scale
(b)Mulliken scale
(c)Allred-Rochow scale
Calculate the electronegativity of Lead using Allred and Rochow Scale
(use Angstrom units)
What is the significance of wave function?
- Solving the schrodinger equation gives the shape of the atomic orbital
- The wave function squared is always positive, hence it gives the probability of finding an electron around the nucleus.
What are the postulates of Bohr’s atomic model?
1.Electrons in an atom behave like a material particle and** revolve around the nucleus in a fixed circular orbit** called stationary states 0r energy levels or energy shells
2.As long as the electron is revolving in a particular orbit it does not emit or absorb energy. Its total energy remains constant hence why these energy levels are also called sationary states
3. Electron can only move in the orbits in which the angular momentum (mvr) of the revolving electron is an integral multiple of h/2π.
i.e., mvr = n(h/2π), n = 1, 2, 3,…
- The equation mvr = nh/2 π means that the angular momentum of the
revolving electron is quantised which implies that the magnitude of the
angular momentum is always a whole number not fraction.
How does the structure of Bohr’s atomic model assist in identifying different elements based on their atomic characteristics?
- different atoms have different energy level arrangements. This produces a unique set of wavelengths of light emitted during transitions from one energy state to another for each atom which can be used to identify atoms.
Why is the energy of an electron negative?
- Electrons in an atom have lower energy than that of free electrons
What are the achievements of Bohr atomic model?
Here’s a breakdown of how Bohr’s atomic model addressed these aspects:
-
Explained the Stability of the Atom:
Bohr proposed that:
- Electrons revolve around the nucleus in fixed, discrete orbits or energy levels, and each orbit is associated with a specific energy.
- As long as the electron remains in a given orbit, it does not radiate energy, overcoming the classical problem of the atom collapsing due to continuous energy loss.
- The quantization of angular momentum ((L = n\hbar)) prevents the electron from spiraling into the nucleus, ensuring the atom’s stability.
-
Explained How Emission Spectrum is Produced:
- When an electron transitions from a higher energy level ((E_2)) to a lower energy level ((E_1)), it releases energy in the form of electromagnetic radiation (photon).
- The energy of the emitted photon corresponds to the difference between the two energy levels:
[
h\nu = E_2 - E_1
]
- This emitted radiation appears as discrete lines in the emission spectrum, characteristic of the atom.
-
Explained How Absorption Spectrum is Produced:
- When an atom absorbs energy (e.g., from light or heat), an electron in a lower energy level ((E_1)) gets excited to a higher energy level ((E_2)).
- The absorbed energy matches the energy difference between the two levels:
[
h\nu = E_2 - E_1
]
- The absorbed wavelengths appear as dark lines in the absorption spectrum, corresponding to the energy required for the transition.
-
Explained the Origin of Spectral Lines in the Hydrogen Spectrum:
- Bohr’s model provided a mathematical explanation for the spectral lines of hydrogen by applying quantized energy levels. The energy of an electron in the (n)-th orbit is given by:
[
E_n = -\frac{13.6}{n^2} \, \text{eV}
]
- The transitions between these energy levels correspond to spectral lines grouped into series, determined by the final orbit ((n_f)) of the electron:
- Lyman Series: Electron transitions to (n_f = 1) (ultraviolet region).
- Balmer Series: Electron transitions to (n_f = 2) (visible region).
- Paschen Series: Electron transitions to (n_f = 3) (infrared region).
- Brackett Series: Electron transitions to (n_f = 4) (infrared region).
- Pfund Series: Electron transitions to (n_f = 5) (infrared region).
Each spectral series arises from specific sets of transitions, producing distinct wavelengths that are unique to hydrogen.
What are the limitations of Bohr’s atomic model?
1) It does not explain the origin of spectra given by multi-electron species.
2) It assumes the circular orbits in which the electrons revolve are planar
instead of 3 dimensional.
3) It does not explain the cause of Zeeman and Stark effects:
1) Zeeman effects- splitting of spectral lines in magnetic field
2) Stark effect - splitting of spectral lines in electric field
4) It does not account for uncertainty principle and dual nature of
electrons.
5) It does not explain the origin of fine structures observed in the spectral
lines using high resolution microscope
Differentiate between the zeeman effect and Stark effect
1)Zeeman effects- splitting of spectral lines in magnetic field
2) Stark effect - splitting of spectral lines in electric field
What is an orbital?
The wave function of an electron
What is an atomic orbital?
The 3-dimensional space where the probability of finding an electron is maximum.
State 5 differences between an orbit and atomic orbitals
|-----------------------|-----------------------------------------|-----------------------------------------------| | Aspect | Orbit | Atomic Orbital | | **Definition** | Circular path for electron movement. | 3D region with maximum electron probability. | **Position** | Exact position of electron known. | Position uncertain due to wave nature. | | **Movement** | Certainty about electron movement. | No certainty of movement. | | **Motion** | Represents Planar motion of an electron.| 3D motion. | | **Max Electrons** | \( 2n^2 \), where \( n \) is orbit no. | Max 2 with opposite spins. | | **Shape** | Always circular. | Varies: \( s \)-spherical, \( p \)-egg-shaped. |
What is a quantum number?
A quantum number is a value used to describe specific properties of electrons in an atom. It defines the state and position of an electron within an atom and determines its energy level, orbital shape, orientation, and spin.
Types of Quantum Numbers:
1. Principal Quantum Number (( n )):
- Represents the main energy level or shell of an electron.
- Values: Positive integers (( n = 1, 2, 3, \dots )).
- Higher ( n ) values indicate electrons are farther from the nucleus and have higher energy.
-
Azimuthal Quantum Number (( l )):
- Describes the shape of the orbital (sub-shell) where the electron is likely found.
- Values: ( l = 0 ) to ( n-1 ).
- Corresponds to sub-shell types:
- ( l = 0 ) (s), ( l = 1 ) (p), ( l = 2 ) (d), ( l = 3 ) (f).
-
Magnetic Quantum Number (( m_l )):
- Specifies the orientation of the orbital in space.
- Values: Integers from ( -l ) to ( +l ) (including 0).
- For example, if ( l = 1 ), ( m_l = -1, 0, +1 ).
-
Spin Quantum Number (( m_s )):
- Describes the intrinsic spin of the electron.
- Values: ( +\frac{1}{2} ) (spin-up) or ( -\frac{1}{2} ) (spin-down).
Importance:
Quantum numbers collectively describe:
- The energy and location of an electron in an atom.
- The behavior and arrangement of electrons, which determines the chemical and physical properties of elements.
What is the minimum atomic number an atom should have before 4dx,
where x represents a positive integer, appears in the atom’s ground-state
configuration? What is the range of values x can take on?
To determine the minimum atomic number (( Z )) at which the ( 4d ) sub-shell starts to appear in the ground-state electron configuration, and the range of ( x ), where ( x ) represents a positive integer for ( 4dx ), let’s break this down:
Step 1: Electron Configuration
- The ( 4d ) sub-shell starts filling after the ( 5s ) sub-shell, according to the Aufbau principle.
- The general filling order for ( n = 4 ) and ( n = 5 ) levels is:
1. ( 4s )
2. ( 3d )
3. ( 4p )
4. ( 5s )
5. ( 4d )
Step 2: Minimum Atomic Number for ( 4d^x )
- The ( 4d ) sub-shell can hold up to 10 electrons (( x = 1 ) to ( x = 10 )).
- To reach the ( 4d ) sub-shell, we need to fill the lower-energy orbitals first:
- ( 1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^{10}, 4p^6, 5s^2 ).
- Total electrons required before ( 4d ) = ( 38 ) (i.e., ( Z = 38 )).
Thus, the ( 4d ) sub-shell begins to appear at atomic number ( Z = 39 ), which corresponds to the element Yttrium (Y), whose configuration is:
[
\text{Y: } [Kr] 5s^2 4d^1
]
Step 3: Range of ( x )
- The ( 4d ) sub-shell can hold up to 10 electrons, so ( x ) can range from ( 1 ) to ( 10 ).
- These correspond to elements with atomic numbers ( 39 ) to ( 48 ):
- ( Z = 39 ) (( 4d^1 )): Yttrium (Y)
- ( Z = 48 ) (( 4d^{10} )): Cadmium (Cd)
Final Answer:
- Minimum atomic number: ( Z = 39 ) (Yttrium, ( 4d^1 )).
- Range of ( x ): ( x = 1 ) to ( 10 ).
