KCL Section 6: Quantum Physics

Question 1

Calculate the wavelength of EM waves with a frequency of:

4. 2 x 1014 Hz
5. 89 x 1011 Hz
6. 05 x 1016 Hz
7. 30 x 1014 Hz
8. 1 x 1015 Hz

Answer 1

Wavelengths:

7. 1 x 10-7 m
8. 09 x 10-4 m
9. 86 x 10-8 m
10. 61 x 10-7 m
11. 4 x 10-7 m

Question 2

Calculate the frequency of EM waves with a wavelength of:
0.00306 m
0.00000543 m
4.28 x 10-9 m
560 nm
0.34 μm

Answer 2

Frequencies:

9. 8 x 1010 Hz
10. 52 x 1013 Hz
11. 01 x 1016 Hz
12. 36 x 1014 Hz
13. 8 x 1014 Hz

Question 3

Describe how a diffraction pattern, like one from a crystal structure, is produced.

Answer 3

Waves are diffracted by the gaps between atoms in the crystal
Diffracted waves interfere with each other
If the waves have a path difference of nλ, where n = integer, the waves will arrive at the detector in phase, and constructive interference will occur, causing a bright spot
If the waves have a path difference of ½nλ, where n = odd integer, the waves will arrive at the detector out of phase, and destructive interference will occur, causing a dark spot

Question 4

In 1924 de Broglie hypothesised that _________ should also behave as waves.

Answer 4

In 1924 de Broglie hypothesised that electrons should also behave as waves.

Question 5

Thomson and Davisson (separately) managed to prove the de Broglie hypothesis by?

Answer 5

Thomson and Davisson (separately) managed to prove the de Broglie hypothesis by firing beams of electrons at metal film and a crystal lattice, respectively.

Question 6

In 1924 de Broglie hypothesised that electrons should also behave as waves.
Thomson and Davisson (separately) managed to prove the de Broglie hypothesis by firing beams of electrons at metal film and a crystal lattice, respectively.
Both scientists found the electron beams produced _________ patterns. The __________ and __________ patterns can only be explained if the electrons were behaving as waves. This provided evidence for wave-particle __________ (and won them the 1937 Physics Nobel Prize)

Answer 6

In 1924 de Broglie hypothesised that electrons should also behave as waves.
Thomson and Davisson (separately) managed to prove the de Broglie hypothesis by firing beams of electrons at metal film and a crystal lattice, respectively.
Both scientists found the electron beams produced diffraction patterns. The constructive and destructive patterns can only be explained if the electrons were behaving as waves. This provided evidence for wave-particle duality (and won them the 1937 Physics Nobel Prize)

Question 7

What did De Broglie link the wavelength of light to?

Answer 7

De Broglie linked the wavelength of light to the momentum of a particle. (remember momentum = mass x velocity)

Question 8

An electronvolt is a unit of what?

Answer 8

An electronvolt is a unit of energy.

Question 9

What is an electronvolt?

Answer 9

It is the amount of energy gained by an electron when it moves through a potential difference of 1 volt.

Question 10

Convert these energies to electronvolts:
1 J
2.3 J
5.4 mJ
8.23 nJ
9.01 x 10-19 J

Answer 10

6 x 10^18 eV

1. 4 x 10^19 eV
2. 4 x 10^16 eV
3. 14 x 10^10 eV
4. 63 eV

Question 11

Convert these energies to joules:
300 eV
12 eV
43 MeV
6.06 GeV
7.78 x 105 eV

Answer 11

4. 80 x 10^-17 J
5. 9 x 10^-18 J
6. 9 x 10^-12 J
7. 70 x 10^-10 J
8. 24 x 10^-13 J

Question 12

19th Century - EM waves considered as waves: Huygens, Hooke and Young all developed explanations for properties of light based on ______ behaviour
Thomson, 1897 - showed electrons are _________, with quantised _______
Maxwell - suggested light and related waves are propagating ________ and magnetic fields
Planck, 1900 - energy is related to _________ of light via E = hf (including a suggestion the light can be quantised)
Einstein, 1905 - photoelectric effect: light must be _______ (confirmed by Millikan)
de Broglie, 1924 - ______________________________________________

Answer 12

19th Century - EM waves considered as waves: Huygens, Hooke and Young all developed explanations for properties of light based on wave behaviour
Thomson, 1897 - showed electrons are particles, with quantised charge
Maxwell - suggested light and related waves are propagating electric and magnetic fields
Planck, 1900 - energy is related to frequency of light via E = hf (including a suggestion the light can be quantised)
Einstein, 1905 - photoelectric effect: light must be quantised (confirmed by Millikan)
de Broglie, 1924 - all matter with momentum has a wavelike nature

Question 13

What is the formula for the energy of a photon

Answer 13

E = hf
This equation links the energy of a photon with the frequency of the complementary wave, via the planck constant h = 6.63 x 10^-34 Js

Question 14

Calculate the energy of EM photons of:
Yellow light with a frequency of 5.2 x 10^14 Hz
Light with a frequency of 4.78 x 10^14 Hz
Microwaves of frequency 3.02 x 10^10 Hz
UV of frequency 1.90 x 10^16 Hz
Gamma of frequency 6.85 x 10^21 Hz

Answer 14

3. 4 x 10^-19 J
4. 17 x 10^-19 J
5. 00 x 10^-23 J
6. 26 x 10^-17 J
7. 54 x 10^-12 J

Question 15

Red light with a wavelength of 700nm
Violet light with a wavelength of 4.15 x 10^-7m
Infrared with a wavelength of 0.79 mm
UV with a wavelength of 3.32 x 10^-8m
X-rays with a wavelength of 0.741 nm

Answer 15

2. 84 x 10^-19 J
3. 79 x 10^-19 J
4. 5 x 10^-22 J
5. 99 x 10^-18 J
6. 68 x 10^-16 J

Question 16

Calculate:
a) the energy, in electron-volts, of a photon of light from a red laser
pointer with a wavelength of 650nm.
b) the wavelength of a 120 keV X-ray.

Answer 16

1.9eV

1 x 10^-11 m

Question 17

Calculate the wavelength of an electron moving at 5.31 x 106 ms-1
What is the wavelength in meters of a proton travelling at 255 000 000 ms-1
Calculate the speed of a neutron with a de Broglie wavelength of 2.6 x 10-10 m. The mass of a neutron is the same as a proton.
The kinetic energy of the electron in a ground-state hydrogen atom is 2.2 x 10-18 J
Show that this suggests an electron momentum of 2.0 x 10-24 kgms-1
Calculate the de Broglie wavelength for an electron with this momentum
The de Broglie wavelength for neutrons used to study crystal structure is 1.23 nm. Calculate the speed of these neutrons.
Calculate the velocity of an electron with a de Broglie wavelength of 269.7 pm

Answer 17

λ = 1.37 x 10-10 m
λ = 1.56 x 10-15 m
v = 15000 ms-1
a. p = 2.00 x 10-24 kgms-1
b. λ = 3.3 x 10-10 m
v = 323 ms-1
v = 2.697 x 106 ms-1

Question 18

De Broglie’s equation shows that the wavelength of an electron depends on its _____________, and its momentum can be increased by increasing the __________ across it.
This means electrons under higher voltages have a __________ wavelength: down to x 10^-10 m, which is a similar scale to an ________.
This allows incredibly detailed _________- far more than with light waves, which are about x 10^-7 m

Answer 18

De Broglie’s equation shows that the wavelength of an electron depends on its momentum, and it’s momentum can be increased by increasing the voltage across it.
This means electrons under higher voltages have a shorter wavelength: down to x 10-10 m, which is a similar scale to an atom.
This allows incredibly detailed microscopy - far more than with light waves, which are about x 10-7 m

Question 19

What is the principle of complementary

Answer 19

The particle and wave properties of objects and EM radiation are complementary, which means that the two types of property cannot be observed or measured at the same time.

This means we can observe light acting as a wave, or as a particle, but not both at the same time.