In 1909, Geiger and Marsden were studying how alpha particles are scattered by a thin gold foil.

Alpha source

Thin gold foil

As expected, most alpha particles were detected at very small scattering angles

Alpha particles

Thin gold foil Small-angle scattering

To their great surprise, they found that some alpha particles (1 in 20 000) had very large scattering angles

Alpha particles

Thin gold foil Small-angle scattering

Large-angle scattering

The results suggested that the positive (repulsive) charge must be concentrated at the centre of the atom. Most alpha particles do not pass close to this so pass undisturbed, only alpha particles passing very close to this small nucleus get repelled backwards (the nucleus must also be very massive for this to happen).

nucleus

Rutherford (their supervisor) calculated theoretically the number of alpha particles that should be scattered at different angles. He found agreement with the experimental results if he assumed the atomic nucleus was confined to a diameter of about 10-15 metres.

In a Geiger Marsden scattering experiment, a nucleus has a diameter of (m) 1.4 x 10-

14

The alpha particle has a mass of (kg) 6.64 x 10-27

What is the kinetic energy of the alpha particle that has a de Broglie wavelength equal to the diameter of the nucleus?

How fast is it traveling?

The same alpha particle is fired at a gold nucleus (Z=79)How close does the alpha particle get to the

nucleus?

That’s 100 000 times smaller than the size of an atom (about 10-10 metres).

If the nucleus of an atom was a ping-pong ball, the atom would be the size of a football stadium (and mostly full of nothing)!

The model has electrons orbiting like planets.

Nucleus (ping-pong ball

According to the theory of electromagnetism, an accelerating charge (and the orbiting electrons ARE accelerating centripetally) should radiate energy and thus spiral into the nucleus.

When a gas is heated to a high temperature, or if an electric current is passed through the gas, it begins to glow.

cathode anode

electric current

Light emitted

Low pressure gas

If we look at the light emitted (using a spectroscope) we see a series of sharp lines of different colours. This is called an emission spectrum.

Similarly, if light is shone through a cold gas, there are sharp dark lines in exactly the same place the bright lines appeared in the emission spectrum.

Some wavelengths missing!Light source gas

Balmer and Rydberg (this version) came up with a formula to show all these energies, but no explanation as to why:

Where R is the Rydberg constant 1.096 x 107 m-1

And the energy is E = hc/

2 2

1 1 1

2R

n

What is the energy of a photon from the Rydberg Equation using n=3?

Scientists had known about these lines since the 19th century, and they had been used to identify elements (including helium in the sun), but scientists could not explain them.

In 1913, a Danish physicist called Niels Bohr realised that the secret of atomic structure lay in its discreteness, that energy could only be absorbed or emitted at certain values.

At school they called me “Bohr

the Bore”!

Bohr realised that the electrons could only be at specific energy levels (or states) around the atom.

We say that the energy of the electron (and thus the atom) can exist in a number of states n=1, n=2, n=3 etc. (Similar to the “shells” or electron orbitals that chemists talk about!)

n = 1

n = 3

n = 2

The energy level diagram of the hydrogen atom according to the Bohr model

n = 1 (the ground state)

n = 2

n = 3

n = 4n = 5

High energy n levels are very close to each other

Energy eV

-13.6

0

Electron can’t have less energy than this

An electron in a higher state than the ground state is called an excited electron.

High energy n levels are very close to each other

n = 1 (the ground state)

n = 2

n = 3

n = 4n = 5

-13.6

Energy eV

0

electron

If a hydrogen atom is in an excited state, it can make a transition to a lower state. Thus an atom in state n = 2 can go to n = 1 (an electron jumps from orbit n = 2 to n = 1)

n = 1 (the ground state)

n = 2

n = 3

n = 4n = 5

-13.6

Energy eV

0

electronWheeee!

Every time an atom (electron in the atom) makes a transition, a single photon of light is emitted.

n = 1 (the ground state)

n = 2

n = 3

n = 4n = 5

-13.6

Energy eV

0

electron

The energy of the photon is equal to the difference in energy (ΔE) between the two states. It is equal to hf. ΔE = hf

n = 1 (the ground state)

n = 2

n = 3

n = 4n = 5

-13.6

Energy eV

0

electron

ΔE = hf

Transitions down to the n = 1 state give a series of spectral lines in the UV region called the Lyman series.

n = 1 (the ground state)

n = 2

n = 3

n = 4n = 5

-13.6

Energy eV

0

Lyman series of spectral lines (UV)

Transitions down to the n = 2 state give a series of spectral lines in the visible region called the Balmer series.

n = 1 (the ground state)

n = 2

n = 3

n = 4n = 5

-13.6

Energy eV

0

UV

Balmer series of spectral lines (visible)

Transitions down to the n = 3 state give a series of spectral lines in the infra-red region called the Pashen series.

n = 1 (the ground state)

n = 2

n = 3

n = 4n = 5

-13.6

Energy eV

0

UV

visible

Pashen series (IR)

The emission and absorption spectrum of hydrogen is thus predicted to contain a line spectrum at very specific wavelengths, a fact verified by experiment.

Which is the emission spectrum and which is the absorption spectrum?

Since the higher states are closer to one another, the wavelengths of the photons emitted tend to be close too. There is a “crowding” of wavelengths at the low wavelength part of the spectrum

n = 1 (the ground state)

n = 2

n = 3

n = 4n = 5

-13.6

Energy eV

0

Spectrum produced

1. Heating to a high temperature

2. Bombarding with electrons

3. Having photons fall on the atom

I’m excited!

1. Can only treat atoms or ions with one electron

2. Does not predict the intensities of the spectral lines

3. Inconsistent with the uncertainty principle (see later!)

4. Does not predict the observed splitting of the spectral lines