T02/024 : ELECTROMAGNETIC RADIATION AND HYDROGEN LINE SPECTRUM Flashcards

Question

What are the conclusions/implications of De Broglie's equation?

Answer 1

- everything in nature exhibits wave and particle properties. - large objects mostly show particle-like behavior. - small objects exhibit wave particles mostly.

Answer 2

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., \( 2s, 2p \).

Answer 3

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.

Answer 4

- flame test - spectroscopy

Answer 5

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

Answer 6

This is a stream of energy moving in the direction of propagation and perpendicular to electric and magnetic field.

Answer 7

- 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.

Answer 8

1. 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. 3. 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

Answer 9

1.Gamma rays 2.X-rays 3.UV Rays 4.Visible Light 5.Infrared rays 6.Microwaves 7.Radio waves

Answer 10

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.

Answer 11

- it is the entire range of electromagnetic radiations separated into different frequencies and wavelengths

Answer 12

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.

Answer 13

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

Answer 14

``` **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).
- Neon signs.
- Astronomical observations (stars). | - Photosynthesis (chlorophyll absorbs specific wavelengths).
- 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.
- Study of excited states of atoms. | - Determining the composition of gases.
- Analyzing solutions or materials (e.g., UV-Vis spectroscopy). | ```

Answer 15

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.

Answer 16

E = hv = hc/λ

Answer 17

- absorption - emission

Answer 18

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

Answer 19

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.

Answer 20

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

Answer 21

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.

Answer 22

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.**

Answer 23

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

Answer 24

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.

Answer 25

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

Answer 26

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.

Answer 27

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

Answer 28

KE = hf - ɸ h=E/f V= (hf - ɸ)/q ɸ = hv = hc/λ (threshold frequency/wavelength)

Answer 29

``` Metal φ (eV) Sodium 2.28 Zinc 4.31 Cobalt 3.90 Silver 4.73 Platinum 6.35 ```

Answer 30

[Ar]4s^1,3d^10

Answer 31

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 ```

Answer 32

**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. 2. **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. 3. **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.

Answer 33

**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

Answer 34

- 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)**

Answer 35

1)Determination

Answer 36

- 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)

Answer 37

- 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

Answer 38

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.

Answer 39

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.

Answer 40

- the first ionization energy is lower than 2nd which is lower than 3rd

Answer 41

(2)Sodium is losing a core electron while Magnesium is losing a valence electron

Answer 42

- the larger the number of protons as compared to e , the smaller the ion - the larger the number of e , the larger the ion

Answer 43

- the higher the negative value the higher the electron affinity - the higher the positive value, the lower the e affinity

Answer 44

1. Solving the schrodinger equation gives the shape of the atomic orbital 2. The wave function squared is always positive, hence it gives the probability of finding an electron around the nucleus.

Answer 45

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.

Answer 46

- 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.

Answer 47

- Electrons in an atom have lower energy than that of free electrons

Answer 48

Here’s a breakdown of how Bohr's atomic model addressed these aspects: 1. **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. --- 2. **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. --- 3. **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. --- 4. **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.

Answer 49

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

Answer 50

1)Zeeman effects- splitting of spectral lines in magnetic field 2) Stark effect - splitting of spectral lines in electric field

Answer 51

The wave function of an electron

Answer 52

The 3-dimensional space where the probability of finding an electron is maximum.

Answer 53

``` |-----------------------|-----------------------------------------|-----------------------------------------------| | 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. | ```

Answer 54

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. 2. **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). 3. **Magnetic Quantum Number (\( m_l \))**: - Specifies the orientation of the orbital in space. - Values: Integers from \( -l \) to \( +l \) (including 0). - For example, if \( l = 1 \), \( m_l = -1, 0, +1 \). 4. **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.

Answer 55

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 \( 10 \).