Atomic spectroscopy and the hydrogen atom

atomic emissions/ rydberg formula/ ionisation energies/ selection rules

Atomic emission

* when atoms heat they glow
* dispersing this light through a prism produces an emission spectrum
* each atom emits light at characteristic and well defined wavelengths

in an atomic emission spectrum, classical mechanics predicts that all wavelengths of light (white light) should be _____

emitted

Hydrogen atom emission

* hydrogen, the simplest atom, has the simplest spectrum
* emission spectrum of atomic H consists of several series of sharp lines.
* lines of each series get closer together at high energy - the series limit

The Rydberg formula

* an empirical formula able to accurately predict the wavenumber value of all H-atom lines

Lymann series

n1 = 1

thus n2 = 2,3,4

UV light

Balmer series

n1 = 2

n2 - 3,4,5…

visible light

Paschen series

n1 = 3

n2 = 4,5,6…

IR spectroscopy

Why are all Rydberg formula for hydrogen atom care so much about integers?

* shows atoms can only have certain discrete energies - energy is quantised

By absorbing or emitting light, atoms can ‘hop’ between energy levels ….

Transitions have to terminate on another energy level

What is the link between energy levels and spectra?

because energy levels of atoms are quantised, EM radiation can only be absorbed or emitted at certain discrete energies

What does the spectra tell us?

spacing between energy levels

What does the spectra not tell us?

the absolute energies of energy levels

Energy levels and spectroscopy

* atoms have many energy levels, giving rise to numerous possible transitions
* the energies of these transitions contribute to the spectrum of the atom
* the spectrum of each atom is unique (an atomic ‘fingerprint’)

When a photon is absorbed, atoms ____ energy

gains

When photons are emitted atoms ____ energy

lose

Emission and absorption spectra give the same information about ____________

Energy level separations

What does the difference in energy between the initial and final energy levels determine?

The frequency of the photon absorbed or emitted

The Bohr frequency condition

Difference in energy = E2 - E1 = hv

If we can derive theoretical expressions for energy levels (quantum mechanics) then we can predict ______

the energies of lights absorbed/emitted (spectroscopy)

Niels Bohr - allowed energy levels of the H atom are

The energy spacing between a level with a principal quantum number n1 and a level with quantum number n2 is :

What does the Bohr’s equation demonstrate?

that the observed transitions are between different electronic energy levels of the H atom

What does the Bohr’s model of the H atom predicts?

that the energy levels get closer together as n → infinity

as a consequence the lines in each spectral series converge to a series limit at high energy

Lowest state is the…

ground state

Anything abut the ground state is the …

Excited state

when n = infinity…

it is ionised

What does the Rydberg formula predicts the __?__

wavenumber and the wavelength of any line in the H atom spectrum

Example: calculate the wavenumber of the first line in the Balmer series

15233 cm-1

What is the ionisation energy?

the minimum energy required to remove an electron completely from an atom

Example: calculate the ionisation energy (in joules) of ground-state H atoms

2\.179 x 10-18 J

Wavenumber to Joules

Wavenumber = difference in energy/ planck’s constant x speed of light

Orbitals is an H atom are…

electronic wavefunctions

orbitals in a H atom are described using…

three quantum numbers

What are the quantum numbers which describe the orbitals in an H atom?

* principle quantum number (n)
* orbital angular momentum (l)
* magnetic quantum number(ml)

Principle quantum number

determines energy and size

n = 1,2,3 …..

Orbital angular momentum

orbital type (s,p,d,f)

l = 0,1,2 … n-1

Magnetic quantum number

orientation of orbital

ml = -l to +l

for hydrogen atoms, energy is only dependent on

the principle quantum number

When an H atom undergoes a spectroscopic transition, the electron _____

jumps between orbitals

In a physical process, there are three fundamental quantities which must be conserved:

1. momentum
2. energy
3. angular momentum

In spectroscopy, the conservation of energy accounted for by?

the Bohr frequency condition

difference in energy = E2 - E1 = hv

In addition to an energy (E = hv) photons also have an ____

intrinsic angular momentum, s=1

what must change in order to compensate, when a photon is observed or emitted?

the angular momentum (l) of the electron in the H atom

What are the forbidden transitions:

1. an electron in a d-orbital (l=2) cannot make a transition to an s-orbital (l=0) - *change in two units of momentum*
2. an electron in as s- orbital cannot make a transition to another s-orbital - *no change in the angular momentum*

The allowed change in angular momentum

if change in l = +- 1, then the transition is allowed

What is a selection rule?

a statement about which spectroscopic transitions are allowed

What are the selection rules for hydrogen (and other 1-electron atoms) ?

/\\n = any value

/\\l = +- 1 (laporte selectrion rule)

/\\ml = 0, +- 1

Grotrian diagrams

* energy of atomic states and the allowed spectroscopic transitions are summarised using grotrian diagrams