Photons and photon energy

A teacher demonstrated the photoelectric effect by illuminating a zinc plate with electromagnetic radiation.

When ultraviolet radiation of wavelength 320 nm was incident upon the zinc plate, electrons were emitted from the zinc surface.

When visible light of wavelength 420 nm was incident upon the zinc plate, no effect was observed.

Explain these observations. Your answer should include calculations.

work function of zinc = 3.74 eV

A pulsar is a rotating neutron star. The pulsar emits electromagnetic radiation as it rotates.

Scientists have recently detected the highest ever energy gamma ray photons received from a pulsar.

The energy of one of these gamma ray photons was determined to be 2.0×10¹³eV.

Calculate the wavelength of these gamma rays.

The pulsar is estimated to be travelling away from the Earth with a velocity

State why this motion away from the Earth does not significantly affect the wavelength of radiation received at the Earth.

Study of the photoelectric effect leads to observations that cannot be explained by the wave theory of light.

When ultraviolet light is shone on a charged zinc plate, electrons are released. When visible light is shone on the zinc plate, electrons are not released.

State what is meant by threshold frequency.

Explain why the observation of a threshold frequency is not consistent with the wave theory of light.

The photoelectric effect can be explained using the idea of photons.

State what is meant by the term photon.

In 1864, William Huggins and William Miller used dark lines in the spectrum of the Sun to identify elements in the Sun’s atmosphere.

*(a) Explain how gases in the Sun’s atmosphere cause dark lines in the spectrum corresponding to different elements.

In 1868, William Huggins analysed light from the star Sirius A. The wavelength of the hydrogen-alpha line for light from Sirius A was slightly different from the hydrogen-alpha line observed from a source in a laboratory.

Huggins suggested that this difference could be explained using the Doppler effect and could be used to determine the speed and direction of the star’s motion relative to the Earth.

Assess Huggins’s suggestion.

Sirius A has a component of velocity away from the Earth of 5.5 km s^–1.

The wavelength of the hydrogen-alpha line observed from a source in the laboratory is 656.46 nm.

Calculate the wavelength of the hydrogen-alpha line as seen in the spectrum of Sirius A.

The photograph below was taken by the James Webb Space Telescope (JWST) and shows a group of galaxies that formed shortly after the big bang, about 1310⁹ years ago.

Derive the equation T = 1/H₀ where T is the age of the universe.

State one assumption made in your derivation.

The parsec (pc) is a unit used for astronomical distances. 1 pc is 3.1×10¹⁶m.

The accepted range for the Hubble constant H₀ is (60–80) km s^–1 Mpc^–1. Deduce whether the observation by the JWST leads to a value of H₀ within the accepted range.

1 year = 3.1610⁷s

The light from one of the galaxies, called Maisie, has a redshift z of 14. The wavelength of light from Maisie detected at the telescope is 4.010^–6m and lies within the infrared section of the electromagnetic spectrum.

Calculate the wavelength of light emitted by Maisie.

Explain why the light emitted by Maisie arrives at the telescope as infrared.

One of the infrared detectors on the JWST is made from material with a work function of 0.30 eV.

Deduce whether this detector can detect the light from Maisie.

In an investigation of the photoelectric effect, electromagnetic radiation of frequency f was directed onto a metal plate. The maximum kinetic energy E of the photoelectrons emitted from the metal plate was determined. The procedure was repeated for a range of frequencies.

The graph shows how E depended upon f.

Determine a value for the Planck constant, h, in J s.

The table gives data for different metal surfaces.

Deduce which metal was being used in the investigation.

The Planck constant can be determined in a school laboratory using light emitting diodes (LEDs).

An LED emits light when the potential difference (p.d.) across it is large enough to transfer sufficient energy to an electron to result in the emission of a photon. The electron must have energy greater than or equal to the photon energy.

The minimum p.d. required to produce light from LEDs emitting different frequencies was measured by increasing the p.d. from zero until light was first seen.

The graph shows the results.

Determine the value of the Planck constant given by this graph.

There are two problems with using LEDs to determine the Planck constant:

• when the p.d. is increased and the LED first emits light it is difficult to see

• the LEDs do not emit a single frequency but also light of frequencies slightly above and below the recorded frequency.

Discuss the extent to which these problems are consistent with obtaining a result from this graph for the Planck constant which is higher than the accepted value.

In 1905 Einstein published his equation for the photoelectric effect.

In 1916 Millikan demonstrated that the maximum kinetic energy of photoelectrons is consistent with Einstein’s equation.

*(a) Discuss the extent to which our current understanding of observations of the photoelectric effect supports the idea that light behaves as photons rather than as waves.

Millikan used his data to obtain a value of the Planck constant.

The following graph of maximum kinetic energy of photoelectrons against frequency was produced from his data for the photoelectric effect using lithium.

Millikan suggested that the uncertainty from his results for lithium was as little as 1%.

Determine whether the value of the Planck constant obtained from this graph is within 1% of the value stated on the data sheet for this examination paper.

Millikan used a device known as a monochromator to ensure that a single wavelength of light was used to illuminate the surface of the lithium. A monochromator separates wavelengths using a diffraction grating.

Calculate the angle at which a diffraction grating would produce the most intense line at a single wavelength of 6.1 × 10⁻⁷m.

number of lines per mm for grating = 600 mm⁻¹

A student has been learning about the photoelectric effect.

The student was asked by his teacher to explain the photoelectric effect. He gave the following explanation:

Discuss whether the student’s answer fully explains the photoelectric effect.

The student sets up a circuit to investigate the photoelectric effect.

The student illuminates the photocell with light of known frequency f. A current is produced in the circuit due to the emitted electrons. He adjusts the potential difference, using a potential divider, until the reading on the milliammeter is zero and records the corresponding reading V_s on the voltmeter. He repeats this procedure for other frequencies of light.

When the reading on the milliammeter is zero the maximum kinetic energy of the emitted electrons is given by eV_s.

Explain how the student can use his results to determine a value for the Planck constant h using a graphical method.

This experiment demonstrates the particle nature of light.

Explain what is meant by the particle nature of light.