Electromagnetic radiation and quantum phenomena

Question 1

Explain what the photoelectric effect is.

Answer 1

1. Free electrons on the surface of the metal absorb energy from the light
2. If enough energy is transferred to an electron, the bonds holding it to the metal break and the electron is released as a photoelectron.

Question 2

What are the three conclusions that were drawn from experimentation on the photoelectric effect?

Answer 2

1. For a given metal, no photoelectrons are emitted if the radiation has a frequency below a value called the threshold frequency.
2. The photoelectrons are emitted with a variety of kinetic energies ranging from zero to some maximum value. The max. value increases with the frequency of radiation and is unaffected by the intensity.
3. The rate of emission of photoelectrons is proportional to the intensity of the radiation.

Question 3

What is the photon model and how does it explain the threshold frequency and max. KE?

Answer 3

• EM waves carry energy in discrete packets called photons. When light hits a metal surface, the metal is bombarded with photons. If one of these photons collides with a free electron, the electron with gain energy equal to hf.
• To leave the metal, this energy gained needs to be greater than or equal to the work function, phi, which is the energy needed to break the bonds holding the free electron in the metal. Therefore: hf >= phi, so the threshold frequency is given by:
  
  • f >= phi/h
• The KE of the electron when it leaves the metal is hf minus any energy is looses as it travels out of the metal. Electrons further from the surface loose more energy hence the range of KEs. For an electron at the surface, the only energy lost is the work function, so hf = KE_max + phi

Question 4

How are the KEs of the photoelectrons and the intensity of the radiation related?

Answer 4

The KE of the electrons is independent of intensity, as each can only absorb one electron at a time. Increasing intensity only increases the number of electrons emitted per second.

Question 5

What is stopping potential (include a formula relating stopping potential and KE_max)?

Answer 5

• The stopping potential, V_s, is the p.d. needed to stop the fastest moving emitted electrons by converting their KE to work done against the applied p.d.
• e*V_s = KE_max

Question 6

What are energy levels?

Answer 6

• Electrons in an atom can only exist in certain well-defined energy levels. Levels are numbered in increasing (less -ve) energies, with n = 1 being the ground state.
• Electrons can move down energy levels by emitting a photon, and they can move up an energy level (excitation) by absorbing a photon. The energy of these photons will be exactly equal to the energy gap between the levels that the electron moves between.

Question 7

What is ionisation?

Answer 7

• When an electron is removed from an atom
• The modulus of the energy of each energy level in an atom gives the amount of energy required to. remove an electron in that level from the atom. The ionisation energy of an atom is the max. energy that could be required to remove an electron i.e. the energy required to remove an electron from the atom from the ground state.

Question 8

How do fluorescent tubes work?

Answer 8

1. An initial high voltage is applied across mercury vapour, accelerating free electrons, which ionise some of the mercury atoms to produce more free electrons.
2. When the free electrons collide with electrons in other mercury atoms, the electrons in the mecury atoms are excited to higher energy levels. When these excited electrons return to their ground states, they emit photons in the UV range.
3. A phosphor coating on the inside of the tube absorbs these photons, exciting its electrons to much higher orbits. As these electrons then cascade down the energy levels, they emit many lower energy photons in the visible light range.

Question 9

What is an electron volt?

Answer 9

• The kinetic energy carried by an electron after it has been accelerated through a potential difference of 1 volt.
• 1 eV = 1.6 * 10^-19 J

Question 10

What type of emission spectra are produced by light from fluorecent tubes and why?

Answer 10

• Line emission spectra
• Electrons in phosphor all move down energy levels with specific energy gaps.
• Photons emitted at specific wavelengths corresponding to these energies.
• Therefore, when this light is split up by a prism, you see a series of bright lines on a black background, with each line corresponding to a specific wavelength of light.

Question 11

What are line absorption spectra and how are they produced?

Answer 11

• Continuous spectrum with black lines in it.
• Formed when white light is passed through a cool gas and then a prism.
• Most electrons in a cool gas will be in the ground state, so they can only absorb photons with energies equivalent to the difference between two energy levels. Photon of the corresponding wavelengths are absorbed to excite them to higher energy levels.
• These wavelengths are therefore missing when the light is split up by the prism, so there are black lines corresponding to the absorbed wavelengths.
• The black lines in an absorption spectrum match up to the bright lines in an emission spectrum of the same gas when it is excited.

Question 12

What does electron diffraction suggest about the nature of electrons?

Answer 12

• Displays wave nature of electrons
• Diffration patterns are observed when accelerated electrons in a vacuum tube interact with spaces in a graphite crystal
• According to wave theory, the spread of lines in the diffraction pattern increases with the wavelength of the wave.
• We can use the de Broglie equation to relate wavelength and momentum, to check if the electrons act like a wave:
  
  • λ = h/mv therefore an increased electron speed should give a smaller wavelength and therefore smaller spread of lines.
• This diffraction behaviour only occurs when the gap that the particle interacts with is similar in size to its de Broglie wavelength.