atomic orbitals (pike) Flashcards
what are the charges of protons electrons and neutrons
proton = 1.6910^-19 faradays constant
electron =-1.6910^-19
neutron = 0
what are the relative charges of protons electrons and neutrons
proton = +1
electron = -1
neutrons = 0
what are the relative masses of protons electrons and neutrons
protons = 1837
electrons = 1
neutrons = 1837
what 2 numbers are atoms characterized by and what do they mean
atomic number Z - number of protons
mass number N - number of neutrons and protons
define isotopes, atomic mass and allotropes
Isotopes - atoms of the same element with a different number of neutrons
Atomic mass (A) - weighted average mass number of all isotopes present
Allotropes - different structural forms of a bulk element due to different spatial arrangement
outline the timeline and development of the atom
1808 - Dalton atom are indivisible
1904 - Thomson electrons surrounded by a soup of positive charge ( plum pudding model)
1911 - Rutherford atoms consisting of electrons moving around a nucleus
1913 - Bohr electrons around the nucleus but only certain energies allowed
post 1930 - Heisenberg orbitals
how do we prove the structure on atoms
One of the best ways of proving the structure of proving the structure of atom is through the interactions with electromagnetic radiation and it is described by its wavelength and frequency
what did louis de Broglie propose
Louis de Broglie proposed that if electromagnetic radiation could exhibit the properties of waves and particles, so could electrons (and every moving particle) also known as wave-particle duality
what is the Heisenberg uncertainty principle
it is not possible to determine the position and momentum of an electron at any particular instant in time
since we cannot determine the exact position and velocity of electrons what do we do instead
calculate the probability of finding an electron in a particular place
what is a node
points where displacement from center is zero
what is a boundary condition
requirement of a wavefunction to have a certain value at a certain point.
quantisation is due to the ends of the strings being fixed
what is the equation for the speed of light
speed of light = wavelength * frequency
speed of light 3*10^8 m/s
define wavelength
the distance between two peaks or two troughs of a wave
describe what happens when behaviors of electromagnetic radiation has properties of a wave
it will have a wavelength and a frequency, and when it goes through a small gap you will get diffraction patterns when you get constructive and destructive interference when two waves get wide
describe what happens when behaviors of electromagnetic radiation has properties of a particle
it has to have a certain mass and it has to have a certain energy and has to have discrete amount of it called quanta (quantisation). particle is a specific amount of energy of one kind of electron
what is the equation for energy of a particle
energy = planks constantfrequency planks constant = 6.2610^-34
describe Bohrs model of the atoms
Bohr introduced the idea of quantisation , and said that the electrons move around the nucleus in orbitals at a fixed distance. each orbit has a fixed radius, is given a quantum number and has a certain energy. the energy of an electro is based upon its quantum number
what happens when an electron moves down to a lower energy level
the excess of energy is emitted as a quantum of light, the change in energy is the change of the quantum of light
why does Bohrs model of quantisation only work for hydrogen
hydrogen only has one electron, when you have more than one electron, with other elements the electrons are going to repel so they are interacting with each other and not just the nucleus
what is the equation for momentum
p=mv
momentum = mass*velocity
how do you measure the position of an electron
needs to interact with a photon, due to the small size of electrons, suitable electromagnetic radiation will be very energetic. photons also have particle - like properties and will change the momentum of electrons
what is an orbital
- Orbitals describe the electron density (probability for finding an electron) in space
cloud of probabilities
what is a wave function
The mathematical function used to calculate the shape of atomic orbitals is called a wavefunction. wavefunctions are a mathematical functions of a position in space and has a single value at each position
what is the fundamental vibration
if a guitar string at both ends the simplest vibrations of the string is the fundamental vibration
for the fundamental vibration what is the wavelength
2L
what is the first harmonic
the first harmonic contains one further stationary point to the fundamental vibration. it consists of two lobes with opposite phases through the vibration + and -
what is the wavelength of the first harmonic
2L/2
what is the second harmonic
the second harmonic contains 2 nodes there are 3 lobes with alternating signs
what is the wavelength of the second harmonic
2L/3
what does solving the schrodinger equation give us
solving the schrodingers equation produces many wavefuctions (electrons can occupy different atomic orbitals if they have enough energy). the equation can only be solved exactly for two body systems, approximations are being used for atoms containing more electrons
why is the value of the wavefunction^2 important
the value of wavefunction^2 at each point in space is proportional to the probability of finding a particle
assumptions about wavefunctions/probability
finite there is a 100% chance of finding an electron in the atom
single valued- there can only be 2 probability of finding an electron at a certain point
continuous
why do we use hydrogen as a model
the hydrogen atom is the simplest. it only has one electron and only experiences one force which is attraction to the nucleus.
schrodingers equation can be solved exactly 2 body system
what is a radial system coordinate
how far is the position from the nucleus regardless of direction
what are the two angular components used to define
the directionand magnitude and both are conserved
what is the radial boundary condition
about the distance to the nucleus r
if an electron belongs to the atom most of its density will be close to the nucleus. The wavefunction has a value the approaches to zero as the distance from the nucleus r increases
exponential decay
how many boundary conditions do we expect for atoms
3D structure so 3 boundary condition
what is the mathematical function of all atomic orbital expressed as
A*e^-Br
where A and B are kinds of constants
- does not depend on coordinates
- has different values for different orbitals
- have the same value everywhere in one orbital
- at large values of r the value of the function is very small so the electron lies close to the nucleus
what is the angular boundary condition
refers to the direction specified by the two angles and the fact that an atom is spherical.
what does the higher number of nodes mean
the higher the energy
the solution with the lowest energy - ground state
the solution with higher energies - excited states
what does a radial node determine
effective size
what do angular nodes determine
their shape
what are the 3 quantum numbers
quantum numbers describe the size and shape of an orbital
1) n - principle quantum number
2) l - angular momentum quantum number/ subsidiary number
3) ml - magnetic quantum number
all whole numbers
what does the principle quantum number tell us
n specifies the total number of nodes (angular and radial) in an orbital and gives an indication of the size and energy of the orbital
how are the total number of nodes calculated
total number of nodes = n-1
what does the angular momentum quantum number tell us
specifies the number of angular nodes in an orbital and describes the shape of the orbital
what is the value of l between
l has an integer value between 0 and n-1
if n=4 l can be 0,1,2 or 3
because there cannot be a higher number of angular nodes then total nodes there is a restriction to the value of l
what does the magnetic quantum number tell us
the ml counts the number of different orbitals that have the same values of n and l and describes the orientation of the orbitals
what is the range of values for ml
ml can have any positive or negative integer between +l and -l
if l=1 ml = -1,0,1
what do the different values of ml represent
represent different orientations of the same shape and energy and are related to the magnetic properties
what is the equation for wavefunction for atomic orbitals
wavefunction = Aangularradial*exponential decay
what is A in the wavefunction equation
A is the normalisation constant, used to put all the orbitals on the same scale.
the value of the constant is different for each orbital
what is the exponential decay in the wavefunction equation
represents the dependence of the wavefunction from the distance to the nucleus
- creates the node at infinity common for all orbitals
- ensures that electrons belong to this atom
makes the value of the wavefunction decrease towards zero when increasing the distance from the nucleus
for the wavefunction equation what happens if either the angular or radial part is missing
use the value of 1
if the equation = 0 what does that tell us
nodes occur when the equation is equal to zero, if any of the terms is equal to 0 the overall function is 0
there are radial nodes when the radial part =0 and there are angular nodes when the angular part = 0
how do we know the number of angular nodes
l= angular nodes
how do we calculate the number of radial nodes
n-1-l
compare the 1s and 2s and 3s orbitals
s orbitals are spherically symmetrical ans have no direction dependence
do not have angular nodes
1s does not have a radial nodes either
2s has one radial node the radial part is expressed at c-r
3s has 2 radial nodes expressed by a polynomical equation two solutions c-dr+r^2
what is the electron density of s orbitals
For an s orbital, the electron density is highest near the nucleus and decreases smoothly as the distance from the nucleus increases. The probability density reaches zero at infinity, indicating that there is a finite probability of finding the electron at any distance from the nucleus within the orbital’s defined boundary
electron density is also proportional to the number of points at which the electron can be at a particular value of r
the number of points is proportional to the surface of a sphere of radius r=4pier^2
how does the radial probability function change for 1s,2s and 3s
increase in size with n
the outermost lobe contains most of the electron density
the electron density is smaller for lobes with a smaller radii
the electron density at the nucleus is very small but not 0
for multi electron atoms what does orbital energy depend on
the orbital energy depends on the quantum numbers n and l not ml
what does the orbital energies depend on for a hydrogen atom
orbital energies depend only on n
for hydrogen if the orbital energy is n what does that mean
2s and 2p are degenerate
3s,3p and 3d are also degenerate
what is absorption
absorption promotes an electron from a lower to an upper energy level
what is emission
emission allows an electron to decay from an upper to a lower level
what does orthogonality mean
they cannot be written as a combination of any others
how can we tell if two wave functions are orthogonal
two wavefunctions are orthogonal if their overlap integral is zero
the overlap integral means that the values of 2 wavefunctions are multiplied at each point and all these values are added up
how does angular nodes cause orthogonality
orthogonality is caused by the relative psoitions of the nodes in the different orbitals
for angular nodes the node is a perfect reflection plane of symmetry
how do radial nodes cause orthogonality
- positive and negative results can be obtained when multiplying the points of 1s by 2s
- when the overlapped positive and negative regions are added together they cancel each other exactly
what is aufbau principle
the ground state electron configuration of an atom is found by putting each electron in turn into the available lowest energy
what is hunds rule of maxiumum capacity
the ground state electron configuration of an atom is the arrangement with the maximum number of spin parallel electrons
what is pauli exclusion principle
every electron must have a unique set of quantum numbers
an orbital cannot contain more than 2 electrons and these must be spin paired to have different ms values
what is spin quantum number ms
related to the intrinsic magnetic moment of an electron
the spin can have 2 possible values + or - 0.5
what is the electrostatic effect on orbital energy for many electron atoms
2s and 2p have different energy
electrons feel electrostatic attraction to the nucleus and repulsion from other electrons
the overall electrostatic effect is that the net attraction to the nucleus is reduced
each electron is partially shielded by other electrons from the full nuclear charge
what is effective nuclear charge
in many electron atoms the nuclear charge than an electron experiences is lower than the true nuclear charge (z)
what is the equation for effective nuclear charge
effective nuclear charge = nuclear charge - shielding
z* = Z-shielding
what happens as the number of electrons increase in terms of Z and Z*
the nuclear charge increases and so foes the effective nuclear charge
what is the equation for the energy of an orbital using Z*
e = -1313(Z*)^2/n^2
define penetration
orbitals overlapping to some extent
what effect does penetration have
increases the nuclear attraction for a 2s electron over than of 2p
decreases the shielding of 2s electrons by 1s electrons
the effective nuclear charge of a 2s would be greater than 2p so 2s are more stable
what are the contributions to the total shielding for slaters rule
0 from all electrons in groups to the right
0.35 from each of the electrons in the same group 0.3 for 1s
0.85 from each electron in the n-1 shell
1 from each electron in lower shells
what is the effects of Z* on atomic radii
from one element to the next, Z increases by 1 but shielding increases by only 0.35. so Z* increases by 0.65 overall the attraction increases making orbital small
what are the valence electrons and what are the shielding effects
those in the outer highest energy quantum level
experiences more shielding than any other electron
generally have the highest value of n
they are responsible for the chemical properties of the atom and are involved in chemical bonding
what are the core electrons and what are the shielding effects
all those in the inner quantum levels
are poorly shielded and experiences a high effective nuclear charge
have lower values of n
unable to take part in chemical properties of chemical bonding
they are important because acts as a shield for the valence electrons
define ionisation energy
energy required to remove the highest energy electron from the atom in the gas phase to produce a cation
what effect does removal of an electron have on shielding
removal of an electron also decreases shielding effects on other electrons so the energies of other electrons change
describe the overall trends going down a group
valence electrons are very well shielded by core electrons
small decrease in ionisation energy down the group
significant increase in atom size
similar physical and chemical properties but not identical
describe the overall trends going across a period
electrons from the same sub-shell dont shield very well so Z* increases rapidly
large increase in ionisation energy across the row
significant decrease in atom size
