AH 3.1.3 The Bohr Model of the Atom, 3.1.4 Wave-Particle Duality & 3.1.5 De Broglie Waves

Question 1

Explain why classical physics could not explain line absorption and emission spectra.

Answer 1

Classical mechanics predicts that when charged particles accelerate or decelerate, they emit EM radiation. An orbiting electron is accelerating because it is moving in a circle and so should radiate energy away causing it to spiral into the nucleus.
As the electron spiralled inwards, its orbit becoming smaller and its velocity greater, the emitted radiation would increase in frequency (energy) causing a spread of emitted wavelengths. However, it had been known from gas discharge experiments in the late 19th century that atoms emitted light at discrete wavelengths (.e. frequencies therefore colours).
So the classical model was wrong (The problem was solved by Neils Bohr).

Question 2

Describe and explain the Bohr model of the atom. Include a labelled diagram in your answer

Answer 2

In the Bohr model of the atom:

1. Electrons orbit the nucleus of the atom.
2. The electrons can only occupy certain allowed orbits (n = 1,2,3 in the diagram).
3. These orbits have definite energies and so are called energy shells or energy levels.
4. In these orbits, the electron’s acceleration does not result in radiation and energy loss as required by classical physics.

Question 3

Describe and explain line absorption and emission spectra using the Bohr model of the atom. Include labelled diagrams in your answer.

Answer 3

Electrons can only gain or lose energy by ‘jumping’ from one allowed orbit to another (a ‘quantum leap’) absorbing or emitting electromagnetic radiation with a frequency f determined by the energy difference of the levels according to the Planck relation:
ΔE = E2 – E1 = hf
The EMISSION of a photon is shown below and results from the downward transition of an electron between levels 3 and 2.
Had the electron ABSORBED a photon of this energy then the electron would have been promoted from level 2 to to level 3.

Question 4

In a hydrogen atom, calculate the velocity of an electron in the first Bohr orbit of radius 5.3 × 10^–11 m.

Answer 4

mvr = nh/2π

v = nh/2πmr

= 1 x 6.63 × 10^-34 / ( 2π x 9.11 × 10^{-31 x} 5.3 × 10^–11 )

v = 2.2 × 10⁶ m s^–1

Question 5

Explain what is meant by wave-particle duality.

Answer 5

Wave-particle duality describes how under certain conditions light behaves as a wave, but under other conditions it behaves as a particle. It does
not make sense in physics to ask what light is; it makes
more sense to ask how it behaves under known conditions.

Question 6

Describe and explain what happens in a double-slit experiment in which photons are sent through one of the slits one by one.

Answer 6

Although only one photon passes through a slit at any given time, gradually the photons hit the detection screen in such a way that a familiar double-slit interference pattern of bright and dark interference fringes in produced.

Question 7

Describe the experimental evidence for wave-particle duality.

Hint - this involves the diffraction of particles.

Answer 7

Electron diffraction is evidence for wave-particle duality. A thin slice of graphite crystal is used as a2-d diffraction grating as shown below.

Question 8

Describe and explain what de Broglie waves are.

Answer 8

The de Broglie hypothesis is that all particles have a wavelength, called the de Broglie wavelength, λ where

λ = h/p = h/mv

h = Planck’s constant
p = momentum of particle
m = mass of particle
v = velocity of particle

Question 9

Use de Broglie waves to explain the wave properties of electrons

Answer 9

Electrons are observed to diffract through thin crystal lattices. To produce such diffraction patterns we must assume the electrons are behaving as waves. This means they should have a wavelength which can be calculated.

Question 10

What is the wavelength of an electron travelling at 3 x 10⁷ ms^-1 in a cathode ray tube?

Answer 10

λ = h/p = h/mv

= 6.63 × 10^–34 / (9.11 × 10^–31 x 3 x 10⁷)

λ = 2.42 x 10^–11 m

Question 11

A neutron and an electron have the same speed. By referring to the de Broglie equation, show which has the longer wavelength?

Answer 11

λ = h/p = h/mv,

so v = =h/m λ

So the electron has the longer wavelength, since it has a smaller mass than the neutron.

Question 12

An electron microscope uses electrons of wavelength of 0.01 nm. What is the required speed of the electrons?

Answer 12

λ = h/p = h/mv

0.04 × 10–9 = (6.63 × 10–34)/(9.11 × 10–31 × v)

v = 1.8 × 10⁷ ms–1