Module 4 Wave Particle Duality

Question 1

What are electrons?

Answer 1

fundamental particles

negative charge of -e

mass in databook (if not travelling close to speed of light)

Question 2

What is the elementary charge e?

Answer 2

the fixed charge e of one electron or proton (1.60x10^-19 Coulomb)

Question 3

What is the evidence of particle behaviour for electrons?

Answer 3

they can gain KE by accelerating

they can be deflected by electric or magnetic fields

they have a fixed mass and charge

Question 4

What is the De Broglie wavelength?

Answer 4

wavelength of a moving particle equal to the ratio of Plancks constant to its momentum (mass x velocity)

Question 5

What is wave particle duality?

Answer 5

some behaviour of electrons is explained using a particle model , some behaviour is explained using a wave model

Question 6

What is rest mass?

Answer 6

the mass of a particle when it is travelling well below the speed of light

Question 7

Explain how the particle properties/behaviour of electrons can be demonstrated using electron diffraction tube equipment

Answer 7

Particle behaviour:
Negative electrons are accelerated through a vacuum to a positive anode at high voltage

Electrons pass through the hole in the anode and produce a beam of electrons with high KE and, momentum and speed

Question 8

Explain how the wave properties/behaviour of electrons can be demonstrated using electron diffraction tube equipment

Answer 8

Wave behaviour:

The beam passes through graphite crystals and diffracts as the De Broglie wavelength is around 1x10^-10m, similar to spacing of carbon atoms in the crystal

The fluorescent screen shows diffraction rings by glowing where the electrons strike the screen (if the De Broglie wavelength is similar to the atomic spacing in the graphite then a lot of diffraction occurs and the rings have a large diameter

This is also an example of interference as the rings show points of minimum and maximum brightness for destructive and constructive interference

Question 9

Why are electrons accelerated by the anode?

Answer 9

electrons have a negative charge, an anode has a positive charge, opposite charges attract

Question 10

What happens if the voltage of an electron is increased, explain

Answer 10

1. they travel faster due to the following
2. W=QV where W is work done in J, Q is Coulombs in C and V is voltage
3. Work done in J = the KE gain of the electrons
4. Therefore if KE is increased in the formula KE=1/2mV^2 — velocity must increase as mass is fixed and momentum p=mv increases
5. De Broglie wavelength =h/p so will decrease and smaller diffraction rings produced

Question 11

What is an electronvolt?

Answer 11

is the energy gained by a single electron travelling through a potential difference of 1 Volt

Question 12

Why is the electronvolt used?

Answer 12

in atomic or quantum physics, values of energy are much smaller than joules. The energy gained in electronvolts is numerically equal to the Voltage V

Question 13

Explain and show how to convert 27eV into Joules

Answer 13

1. W=QV (W in joules, Q in coulombs, V in volts)
2. When V =1V and Q = 1.60x10^-19 C then W = 1.60x10^-19 J. This is 1 eV in Joules and is given in the formula book
3. Then 27eV = 4.32x10^-18J

Question 14

What does P.D. stand for?

Answer 14

potential difference in volts

Question 15

Why can the electronvolt be used for protons?

Answer 15

they have the same magnitude of charge e = 1.60x10^-19 C

Question 16

Describe and explain the effect of doubling the voltage of an electron? (electron diffraction)

Answer 16

Doubling the voltage doubles the KE as W=QV, W and KE are both in joules (V here is voltage)

KE=1/2mv^2

v speed is increased by √2

λ=h/mv so λ will decrease by 1/√2

in diffraction rings, increasing speed of electron decreases diameter of rings

Question 17

What is the De Broglie wavelength of a person of mass 60kg moving at 1 m/s

Answer 17

De Broglie wavelength=6.63x10^-34/ 1x60
=1.105x10-35m
This is too small to detect diffraction effects

Question 18

What is the significance of the de Broglie wavelength for large mass objects in terms of wave behaviour?

Answer 18

De Broglie wavelength is extremely small compared to size of apertures large mass objects can pass through

Large mass objects do not show wave behaviour as diffraction requires wavelength and aperture to be of a similar magnitude therefore they do not diffract