Electromagnetic Radiation and Quantum Phenomena

Question 1

What is the photoelectric effect?

Answer 1

Free electrons on the surface of a metal absorb light.
If an electron absorbs enough energy (work function) the bonds holding the electron to the metal break and the electron is released (this is then called a photoelectron).

Question 2

What are the 3 main conclusions from the photoelectric effect experiment?

Answer 2

1. For a given metal, no photoelectrons are emitted if the radiation has a frequency below a certain value (the threshold frequency).
2. The photoelectrons emitted will have a range of kinetic energies ranging from 0 to some maximum value. The value of the maximum kinetic energy increases with the frequency of the radiation, and is unaffected by the intensity of the radiation.
3. The no. of photoelectrons emitted per second is proportional to the intensity of the radiation.

Question 3

What is the wave theory (explains conclusion 3 of photoelectric effect experiment)?

Answer 3

• For a particular frequency, the energy carried is proportional to the intensity of the beam.
• The energy carried by the light will be evenly spread over the wavefront.
• Each free electron on the surface of the metal would gain a bit of energy from each incoming wave.
• Gradually, each electron would gain enough energy to be released from the metal.

Question 4

What is the work function?

Answer 4

The amount of energy needed to break the bonds holding the electron against the metal.

Question 5

Explain why the photoelectric emission from a metal surface only occurs when the frequency of the radiation exceeds a certain threshold value.

Answer 5

• If the energy gained by an electron from a photon is greater than the work function, the electron is emitted.
• If it isn’t, the metal will heat up, but no electrons will be emitted.

Question 6

What is the formula for threshold frequency?

Answer 6

f = phii / h

Question 7

What is the kinetic energy the electron will be carrying when it leaves the metal?

Answer 7

Hf - any energy it lost on the way
(p.s., electrons deeper in the metal will lose more energy than the electrons on the surface).

Question 8

Is the kinetic energy of the electrons independent or dependent of the intensity?

Answer 8

Independent because they can only absorb one photon at a time. Increasing the intensity just means more photons per second on an area, the energy is still the same as before.

Question 9

What is the maximum kinetic energy of a photoelectron?

Answer 9

Ek (max) = hf - phii

Question 10

What is the stopping potential?

Answer 10

The potential difference needed to stop the fastest moving electrons with Ek (max).

Question 11

What is the formula for stopping potential?

Answer 11

Charge x stopping potential = Ek (max)

Question 12

How are the emitted electrons made to lose their energy?

Answer 12

By doing work against an applied potential difference.

Question 13

How do fluorescent tubes use excited electrons to produce light?

Answer 13

• Fluorescent tubes contain mercury vapour, across which an initial high voltage is applied. This voltage accelerates fast-moving free electrons which ionise some of the mercury atoms, producing more free electrons.
• When this flow of free electrons collides with the electrons in other mercury atoms, the electrons in the mercury atoms become excited.
• When these excited electrons return to their ground state they emit photons in the UV range.
• A phosphor coating on the inside of the tube absorbs these photons, exciting its electrons to much higher orbits. These electrons can then cascade down the energy levels emitting many lower-energy photons in the form of visible light.

Question 14

Line emission spectra:

Answer 14

• If you split the light from a fluorescent tube with a prism or a diffraction grating, you get a line spectrum.
• A line spectrum can be seen as a series of bright lines against a black background.
• Each line corresponds to a particular wavelength emitted by the source.
• Since only certain photon energies are allowed, you can only see the wavelengths corresponding to these energies.

Question 15

Continuous spectra:

Answer 15

• The spectrum of white light is continuous.
• If you split the light up with a prism, the colours all merge into each other.
• Hot things emit a continuous spectrum in the visible and infrared.
• All the wavelengths are allowed because the electrons are not confined to energy levels in the object that has produced the continuous spectrum. The electrons are not bound to atoms and are free.

Question 16

Explain how you get a line absorption spectrum when light with a continuous spectrum of energy (white light) passes through a cool gas?

Answer 16

• At low temperatures, most of the electrons in the gas atoms will be at their ground states.
• Photons of the corresponding wavelengths are absorbed by the electrons to excite them to higher energy levels.
• These wavelengths are then missing from the continuous spectrum when it comes out the other side of the gas (represented by a continuous spectrum with black lines in it corresponding to the absorbed wavelengths).

Question 17

What is the result of comparing an absorption and emission spectra of a particular gas?

Answer 17

The black lines from the absorption spectra match up with the bright lines from the emission spectra.

Question 18

Interference and diffraction show light behaving as a wave:

Answer 18

• Light produces interference and diffraction patterns (alternating bands of light and dark).
• This can only be explained using waves interfering constructively (when two waves overlap in a phase), or interfering destructively (when the two waves are out of phase).

Question 19

The photoelectric effect shows light behaving as a particle:

Answer 19

• Einstein explained the results of the photoelectricity effect by thinking of the beam of light as a series of particle-like photons.
• If a photon is a discrete bundle of energy, then it can interact with an electron in a one-to-one way, where all the energy from the photon is given to the electron.

Question 20

What is De Broglie’s wave-particle duality theory?

Answer 20

If wave-like light shows particle properties (photons), then particles like electrons should be expected to show wave-like properties.

Question 21

What is the equation for de Broglie wavelength?

Answer 21

Wavelength = h/mv
Where mv = p

Question 22

What can the de Broglie wave of a particle be interpreted as?

Answer 22

A probability wave.

Question 23

How can you observe the wave properties of electrons?

Answer 23

• Using electron diffraction patterns.
• These are observed when accelerated electrons in a vacuum tube interact with the spaces in a graphite crystal.

Question 24

How can you use electron diffraction patterns to show that electrons inhibit wave-like properties?

Answer 24

• According to the wave theory, the spread of the lines in a diffraction pattern increases if the wavelength of the wave is greater.
• In an electron diffraction experiment, a smaller accelerating voltage (slower electrons), give larger spaced rings.
• Therefore, increasing the speed of the electrons means the diffraction pattern circles squash together in the middle.
• This links to the de Broglie wavelength equation: if momentum is increased, then wavelength is decreased, and therefore the spread of the diffraction pattern lines is decreased.
If a particle of greater mass is travelling at the same speed as the electrons, then it would have a tighter-packed diffraction pattern because it would have a larger momentum, giving a smaller wavelength which gives a tighter-packed diffraction pattern.

Question 25

Finish the statement:
In general, the wavelength of accelerated electrons in a vacuum tube is about the same size as..

Answer 25

the electromagnetic waves in the X-ray part of the spectrum.

Question 26

Why don’t particles always show wave-like properties?

Answer 26

Because diffraction only occurs when a particle interacts with an object the same size as its de Broglie wavelength. (vice versa)