Describe atomic spectroscopy

The study of the absorption and emission of photons by atoms. Experimental observation prompted the idea that energy is quantised.

Give the equation that governs which energies are possible for the hydrogen atom and explain all the terms

E is measured in joules

h is planck's constant

c is the speed of light

Rh is the Rhydberg constant for the H atom

n is the principle quantum number

Describe what happens when an electron is excited to a higher energy state

The atom absorbs a specific amount of energy equal to the separation of the levels. (E2-E1 = hf = hv - h is planck's constant and f is v (nu) is the frequency)

Describe what happens when an electron drops down to a lower energy state

The atom emits a specific amount of energy equal to the separation of the levels (E2-E1 = hf = hv - h is planck's constant and f is v (nu) is the frequency)

State the equation for photon energy

Photon energy = hf = E2 - E1 = hv (should be a very small number) E2 is the higher energy f is v (nu) is the frequency

Describe absorption spectra

Absorption spectra measure the wavelengths of light that are absorbed by a sample, as the atoms take up energy and move to higher energy levels. All species start in their ground state

Describe how emission spectra are obtained

Energy is put into a sample of atoms to excite them to higher levels. The wavelengths of the light emitted when the atoms give up energy and drop back down is measured

Describe how energy is given to a sample of atoms in emission spectra

The sample is heated or an electrical discharge is applied

State the four components needed to carry out a typical absorption spectroscopic experiment

- a light source

- a sample

- a wavelength selecting element

- detector

Describe the light source needed in a typical absorption spectroscopic experiment

As there has to be a broad range of wavelengths produced, white light is used

Describe the sample needed in a typical absorption spectroscopic experiment

The sample normally has to be gaseous, which means it must be heated beforehand

Describe the wavelength selecting element needed in a typical absorption spectroscopic experiment and give two examples.

This is needed to disperse the light that has passed through the sample, in order to see which wavelengths of light have been absorbed. A prism or a diffraction grating may be used.

Describe the detector needed in a typical absorption spectroscopic experiment

In the past, photographic plates were used but now highly sensitive cameras are more common. Sometimes the selecting element is rotated and a point detector is used.

Describe the setup of a typical emission spectroscopic experiment

- A sample

- a wavelength selecting element

- detector

The sample is excited and the wavelength selecting element disperses the wavelengths.

The setup is almost the same as that of an absorption spectroscopic experiment, but without the light source.

Describe atomic spectra

The lines show how the electronic energy of atoms is quantised. Different atoms have different spectra, so they can be used to identify elements

Name in order the EM spectrum starting from the lower energy waves

Radiowaves, microwaves, infrared, visable, ultra violet, x-rays, gamma rays

Define an electron volt (eV)

The energy gained by the charge of a single electron moved across an electric P.D of one volt. It is 1.602x10^{-19} J

Describe how to convert from joules to eV

Divide energy in joules by the value of 1 eV

State the fundamental equation for the speed of an EM wave

c = fλ

c is the speed of the wave f is the frequency λ is the wavelength

State the multiplier for the prefix 'nano'

10^{-9}

Define one Å

Å represents 'angstrom'. One angstrom = 1x10^{-10}m

Define wavenumber (v~) and relate it to photon energy

1/λ, measured in (length)^{-1}. We can get E = hcv~, so photon energy is proportional to wavenumber. It is an energy equivalent unit

State how to convert from m^{-1} to cm^{-1}

Divide by 100

Describe the emission spectra of the hydrogen atom

There are many lines which are clearly in groups (ie series), with each series of lines converging with decreasing wavelengths/ an increasing photon energy. All lines in a series have the same value of n_{1}. The names correspond to the scientists who observed them.

Give Bohr's equation for wavenumber and explain the terms

R_{H} is the Rydberg constant for the hydrogen atom.

n_{2} is the quantum number of the upper level of the transition and n_{1 }the number of the lower level. n_{2} > n_{1}

State the names of the first four series and their values of n_{1}

Lyman (n_{1} = 1), Balmer (n_{1 }= 2) , Paschen (n_{1} = 3) and Brackett (n_{1} = 4)

Describe Bohr's explanation of his equation for wavenumber

He said the electron orbiting the nucleus must be confined to specific orbits of fixed energies, with each orbit having a different value of n

Give the energy level expression for the hydrogen atom in joules and wavenumbers

n is the principle quantum number

Define the zero of energy

Also known as the ionisation limit, where n = ∞, this is defined as a separated proton and electron. From this we can see why orbital energies are negative.

Describe how to determine the value of R in the energy level expression for an atom

Start by looking at values of wavenumber of lines in one series; all values of n1 will be the same so 1/n_{1}^{2} can be labelled as a constant c. Now the Bohr equation resembles that of a straight line, and -R can be found by calculating the gradient of this line

Describe the Rydberg constant

R_{x }is calculated using values of wavenumber for a particular atom. It differs slightly for different atoms.

Describe Bohr's three postulates that quantitatively explain the energy level equation for the hydrogen atom

- Electrons move in circular orbits around the nucleus

- Only certain orbits are allowed, ie those with integer values of n. While in these orbits, electrons do not emit energy.

- A single photon is emitted or absorbed when an electron moves into a different orbital

Give the equation that gives the force required to keep a particle in its circular orbit and explain the terms

F = force

m = mass of the particle

v = velocity of the particle

r = radius of the orbit

Note the negative sign: force is in the opposite direction to the radius, ie it points towards the centre of the orbit

Give the equation for linear momentum

p = mv

p = momentum

m = mass

v = velocity

Describe angular momentum

It is a vector quantity and its direction is perpendicular to the plane of rotation. It is important as electrons and photons have angular momentum which is usually conserved in chemical processes.

Give the equation for angular momentum and explain the terms

L = Iω

I is the moment of inertia; the angular equivalent of mass

ω (omega) is the angular velocity in rads-1

Describe I, the moment of inertia

l is the sum over all the masses that make up the body multiplied by the square of their distance from the axis of rotation. Ie heavy objects with a lot of mass far from the axis of rotation have a large moment of inertia

Describe kinetic energy and give its equation

Kinetic energy is energy due to movement and is equal to 1/2mv^{2}

Describe potential energy (V)

V is energy because of a position in a field. It is a relative quantity and is calculated by how much work is takes to move the object from a defined 'zero state'.

State coulomb's law and explain its use and its terms

This equation tells us about the force between two charged species.

State Bohr's postulate relating to the quantisation of the angular momentum of the electron

Bohr said the angular momentum of the electron had to have values of multiples of h/2⫪, = ℏ. Ie nℏ where n was the quantum number. Note; if we rearrange this to get v, it is shown that the velocity of the orbiting electron is also quantised.

Describe the zero state and potential energy of the hydrogen atom.

'Zero State' is defined as infinite separation. As the electron gets closer to the nucleus, P.E becomes negative. Work has to be done on the system to separate the electron and the proton; work done to move an electron from a distance r from the nucleus to infinite separation is measured in joules and equal to -V

Describe kinetic energy and give its equation

Kinetic energy is energy due to movement, and is equal to 1/2mv^{2}

State the two types of energy an object can have

Kinetic and/or potential

Give the equation for potential energy (V) of an electron and explain the terms

e is the fundamental charge, 1.602 x 10^{-19} C

ε_{0} is the permittivity of free space, 8.854 x 10^{-12} Fm^{-1}

r is the radius

Define the ionisation energy of an atom

The energy required to remove an electron from the ground state of the atom to an infinite distance.

Define the ionisation energy of an orbital

The energy required to remove an electron from that orbital to an infinite distance, ie exciting the electron from that orbital to one with n = ∞

Give the equation for the ionisation energy of an electron in a specified Hydrogen orbital

Note: for all atoms except hydrogen, this equation must be multiplied by Z^{2}

This equation gives IE in cm^{-1}

Describe the principle quantum number, n

n can take any positive integer value. For the H atom, it determines the energy.

Describe the orbital angular momentum quantum number, l

l tells us about the orbital angular momentum of the electron, ie how fast the electron orbits the nucleus. l can take integral values from 0 to n-1

Describe the magnetic quantum number (m_{l})

ml tells us the component of the orbital angular momentum along the z-axis, and that component is quantised. m_{l} can take integer values between and including -l to +l.

Give the meaning of 'the orientation of l is quantised'

Give the equation for the magnitude of the orbital angular momentum, ie the length of l

State the selection rule for n in an absorption spectrum

There is no restriction on the change of n

State the selection rule for l in an absorption spectrum

State the selection rule for m_{l} in an absorption spectrum

Describe the transitions in absorption

1s --> np

State how many independent wavefunctions/orbitals there are for any value of l

For a given value of l, there are 2l+1 independent wavefunctions/orbitals.

Give the factor by which the strength of the spin-orbit interaction increases

Z^{4}

Therefore, splittings are more obvious with heavier atoms

Define the total angular momentum quantum number, j

j comes from combining the orbital l and spin angular momentum s.

j = l+s, l+s-1, ... |l-s| - this is a Clebsh-Gordon Series

j is quantised

State the value of s when we are dealing with just one electron, eg in an H atom

s = 1/2

Give a standard term symbol

^{2s+1}l_{j}

_{l is given as a capital letter, ie if l = 0, it is written as S }

Note that for multi-electron atoms, total spin angular momentum and total orbital angular momentum are obtained by combining s and l values of all the electrons.

State the selection rule for s

State the selection rule for j

Describe the fine structure of a transition

The fine structure of a transition is due to spin-orbit coupling. Splitting patterns are very small and observing them requires high-resolution spectroscopic techniques.

Describe the quantised orientation of j, m_{j }

m_{j }can take values from j down in steps of 1 to -j

Note that in the absence of an external field, all m_{j} sublevels of a given j state are degenerate

Describe how the degeneracy of the m_{j} levels is affected in an external field, ie in a magnetic or electric field

The degeneracy of the m_{j} levels is removed and the atomic spectra exhibit many more lines

Describe the Zeeman effect

The Zeeman effect refers to the increased complexity of the atomic spectrum in a magnetic field

Describe the Stark effect

The Stark effect refers to the separation of the m_{j} levels due to an electric field

Describe the anomalous Zeeman effect

The anomalous Zeeman effect applies to atoms which have non-zero spin angular momentum, s>0

Give the equation giving the energies of the mj sublevels of a given j state in a magnetic field

k is a constant which depends on the size of the magnetic field (B) and other constants.

g_{j} is the Lande g - factor

Splitting is proportional to m_{j }so larger values of m_{j} are shifted the most, and positive values of m_{j }are shifted to higher energy, and visa versa

Define the Lande g - factor

The splitting between the different m_{j }levels of a given j state at a given field is given by g_{j}.

Larger values of g_{j} mean larger amounts of splitting.

The values of l, j and s put into the equation are the values for the level we are considering

Give the equation for the reduced mass of a system, μ

m_{e} is the mass of an electron and m_{n} is the mass of the nucleus

State the selection rule for m_{j}

State the contribution of a closed (ie complete) shell to the angular momentum of an atom

A closed shell contributes no angular momentum to an atom

Describe how to construct term symbols for multielectron atoms

Only electrons in partly filled orbitals are considered.

S and L are the total spin and orbital angular momentum of the atom, and s_{i} and l_{i} are the spin and orbital angular momentua of the electrons of interest, i = 1,2,3...

S and L are combined to give J

Define δ_{nl }

δ_{nl }is called the quantum defect. Its value heavily depends on l and very weakly depends on n.

It quantifies the degree of penetration of an electron in a given orbital.

Give the energy level expression used to model the spectra of sodium

Describe how term symbols for the helium atom are worked out

We use a Clebsh-Gordon Series to combine the spins and orbital angular momenta of the individual electrons to get S and L

S = s_{1}+s_{2}, s_{1}+s_{2}-1, |s_{1}-s_{2}|

L = l_{1}+l_{2}, l_{1}+l_{2}-1, |l_{1}-l_{2}|

State and describe the selection rules for multi-electron atoms

The selection rules for S and J are the same as those for s and j, note that the selection rule for L is different to that of l

ΔS = 0

ΔJ = 0, ±1

ΔL = 0, ±1

State the name for states with S = 1

Triplet states, as 2S + 1 = 3

State the name for states with S = 0

Singlet states, as 2S + 1 = 1

Give μ for an infinitely heavy nucleus

μ = m_{e}

For the case that m_{e}<