Quantum Physics (DP IB Physics)

True.

A photon with a frequency greater than the threshold frequency of a metal will also have an energy greater than the work function of the metal.

This is because the energy of a photon is directly proportional to its frequency.

When a photon has an energy greater than the work function of the metal, a photoelectron is released from the metal and the surplus energy is transferred to the kinetic energy of the photoelectron.

The photoelectric equation is

Where:

• = Planck constant, measured in joule seconds (J s)

• = frequency of photon, measured in hertz (Hz)

• = work function of metal, measured in joules (J) or electronvolts (eV)

• = kinetic energy of photoelectron, measured in joules (J)

The photoelectric equation is

Where:

• = kinetic energy of photoelectron, measured in joules (J)

• = Planck constant, measured in joule seconds (J s)

• = frequency of photon, measured in hertz (Hz)

• = work function of metal, measured in joules (J) or electronvolts (eV)

True.

A photoelectron that only just escapes the surface of the metal will have zero kinetic energy.

True.

A photon that does not have enough energy to overcome the work function will not liberate any electrons from the surface of the metal.

False.

The majority of photoelectrons will have energies less than .

True.

A photon with a frequency equal to the threshold frequency will be able to liberate an electron from the surface of the metal, but that photoelectron will have a kinetic energy of zero.

True.

The maximum kinetic energy of a photoelectron is independent of the intensity of the radiation.

False.

The maximum kinetic energy of a photoelectron depends only on the frequency of the incident photon.

The equation for the maximum kinetic energy of a photoelectron is

Where:

• = kinetic energy of photoelectron, measured in joules (J)

• = electron rest mass, measured in kilograms (kg)

• = maximum velocity of photoelectron, measured in metres per second (m s^–1)

The kinetic energy of a photoelectron is independent of the intensity of the incident radiation because each electron can only absorb one photon.

The kinetic energy of the photoelectrons varies because some of the electrons are closer to the surface of the metal than others.

Those that are closer to the surface require less energy to escape and therefore have more surplus energy left over from the photon.

The photoelectric current is a measure of the number of photoelectrons emitted per second from the surface of a metal undergoing the photoelectric effect.

True.

Photoelectric current is proportional to the intensity of the incident radiation.

Stopping potential is the potential difference required to stop photoelectron emission from occurring.

The stopping potential provides information about the maximum kinetic energy of the photoelectrons.

A gold leaf electroscope can be used to demonstrate the photoelectric effect.

To show the photoelectric effect using a gold leaf electroscope:

• the metal plate is given a negative charge

• the gold leaf is repelled

• UV light is shone onto the metal plate

• photoelectrons are emitted

• the gold leaf is no longer repelled

True.

In the gold leaf electroscope demonstration, the gold leaf begins to fall down instantly when illuminated with UV light. This is evidence for the one-to-one quantised transfer of energy from photon to electron.

False.

In the gold leaf electroscope demonstration, the gold leaf does take longer to fall at low intensities of UV light, but it does still happen instantly.

True.

In the gold leaf electroscope demonstration, the gold leaf does not fall down when lower frequencies of light are used.

This provides evidence for the threshold frequency and work function of metals.

False.

In the gold leaf electroscope demonstration, the gold leaf does not fall when the intensity of the light is increased if the frequency is lower than the threshold frequency.

This provides evidence for the threshold frequency and work function.

False.

Wave theory cannot be used to explain the photoelectric effect; the wave model predicts that:

• photoelectrons would be released at any frequency because energy would be accumulated by the electron with each wavefront

• the kinetic energy of the emitted photoelectrons should be dependent on the intensity because, for a given frequency, the energy of a wave is proportional to the intensity of the light

True.

Louis de Broglie proposed that electrons could behave like waves, based on the idea that waves (light) can behave like particles (photons).

The de Broglie wavelength is the wavelength associated with a moving particle.

The equation for the de Broglie wavelength is:

Where:

• = de Broglie wavelength, measured in metres (m)

• = Planck constant (6.63 × 10^-34 J s)

• = momentum, measured in kilogram metres per second (kg m s^–1)

Momentum derived from the kinetic energy equation as follows:

The equation linking the de Broglie wavelength and the kinetic energy of the moving particle

Where:

• = de Broglie wavelength, measured in metres (m)

• = Planck constant (6.63 × 10^-34 J s)

• = mass of the particle, measured in kilograms (kg)

• = kinetic energy of the particle, measured in joules (J)

True.

For everyday objects travelling at normal speeds, the de Broglie wavelength is far too small for any quantum effects to be observed.

True.

The quantum effects of electron diffraction will only be observable when the width of the aperture is of a similar size to the de Broglie wavelength.

The type of atomic lattice usually used to demonstrate electron diffraction is graphite film because of its crystalline structure.

The diffraction pattern produced from electron diffraction is a series of concentric rings.

As the voltage applied to the electron diffraction tube is increased:

• the speed of the electrons increases

• the momentum of the electrons increases

• the kinetic energy of the electrons increases

• the de Broglie wavelength decreases

• the angle of diffraction decreases

• therefore, the radius of the diffraction pattern decreases

Wave-particle duality is the theory that light can behave as a particle and as a wave.

One experiment that provides evidence that light behaves like a wave is Young's double slit experiment.

One experiment that provides evidence that light behaves like a particle is the photoelectric effect.

Newton proposed the corpuscular theory of light in 1672, which first described light as particle-like.

Huygens proposed the wavelet theory of light in 1690, which first described light as a wave.

Young proved that light has wave-like behaviour in 1803 with his double slit diffraction experiment.

Hertz first observed the photoelectric effect in 1887, proving that light also has particle-like behaviour.

Planck first proposed the idea of quantised energy around 1900 when he identified the Planck constant.

Einstein proposed that light can be described as discrete quanta of energy that behaves like particles in 1905.

De Broglie proposed wave-particle duality in 1924 and theorised the de Broglie wavelength.

The Compton effect is the interaction of a high-energy photon with an orbital electron, which causes an increase in the wavelength of the photon and the ejection of the electron.

Compton scattering provides evidence for the particle nature of light.

False.

Compton scattering cannot be explained by considering the incident X-rays as waves. It can only be explained using a particle model.

In Compton scattering:

• a photon collides with an orbital electron and transfers some of its energy

• the wavelength of the photon increases because its energy decreases

• the photon is deflected from its initial path

• the electron is ejected from the atom

False.

In Compton scattering, the electron and photon are deflected in different directions due to conservation of momentum.

The equation for Compton scattering is

Where:

• = change in wavelength of the photon, measured in metres (m)

• = Planck constant (6.63 × 10^-34 J s)

• = rest mass of an electron (9.11 × 10^-31 kg)

• = speed of light (3.00 × 10⁸ m s^–1)

The constant is called the Compton wavelength.

Conservation of energy in Compton scattering:

• energy before = initial photon energy =

• energy after = final photon energy + electron energy =

• energy before = energy after, or