Photons & photon energy

Show that each X‑ray photon produces about 2000 light photons.

The photocathode has a work function of 2.3 eV.

Explain what is meant by the work function.

Calculate the maximum kinetic energy of the electrons leaving the photocathode.

12 X‑ray photons are detected every minute.

Use your answer to (a) to calculate the current I leaving the photocathode. Assume that all the photons of light produce photoelectrons.

State one other assumption you have made to enable you to calculate the current I in (b)(iii).

A light-emitting diode (LED) can be used to determine the Planck constant h. When the LED just starts to emit light, the equation below is valid

where V is the potential difference (p.d.) across the LED, is the wavelength of the light emitted, c is the speed of light in vacuum and e is the elementary charge.

In the equation above, is the energy of a photon emitted from the LED.

Determine the S.I. base units for h.

* Describe how an experiment can be carried out in the laboratory to determine h from a graph. Your description must include how V and are accurately determined. Assume that the

values of e and c are known.

Additional answer space if required

Calculate the work function of potassium in eV.

This question is about a photoelectron emitted perpendicular to plate E and with an initial kinetic energy of 4.8 × 10^–20 J.

Show that the magnitude of deceleration of this photoelectron is 8.8 × 10¹² m s^–2. (i)

Show that the initial speed of the photoelectron is about 3 × 10⁵ m s^–1. (ii)

Calculate the time t taken by the photoelectron to travel from plate E to plate C.

Using the axes shown below, sketch a graph of kinetic energy E_k against distance x from plate E.

Explain, in terms of photons, what happens to the ammeter reading when light of frequency greater than 6.3 × 10¹⁴ Hz is now incident on plate E.

Describe the origin of the microwave background radiation.

The figure below shows how the intensity of the microwave background radiation varies with its wavelength .

The peak intensity is at a wavelength of 1.1 mm.

This spectrum of microwave background radiation changes with temperature according to Wien’s displacement law.

Suggest and explain how the spectrum might have looked in the distant past. You may draw on the figure to support your answer.

Calculate the energy of a photon which has a wavelength of 1.1 mm.

Estimate the number of photons of microwave background radiation incident per second on the back of your hand.

Assume that all emitted photons have the energy calculated in (ii), and that the back of your hand has a surface area of 150 cm².

number of photons per second =........ s^–1

Define the work function of a metal.

The work function of potassium is 2.3 eV.

Potassium emits electrons from its surface when blue light is incident on it. Extremely intense red light produces no electrons.

Explain these observations in terms of photons and their energy.

Light from a laser is incident on some potassium in a vacuum. Electrons are emitted. The wavelength of the light is 320 nm.

Calculate the shortest de Broglie wavelength of the emitted electrons.

A light-emitting diode (LED) emits red light when it is positively biased and has a potential difference (p.d.) greater than about 1.8 V.

The energy of a photon of red light is about 1.8 eV.

Calculate the wavelength of this red light.

The LED is connected into a circuit, as shown below.

The battery has electromotive force (e.m.f.) 4.5 V and negligible internal resistance. The resistor R has resistance 150 . Assume the p.d. across the LED is 1.8 V.

The diagram below shows a circuit designed by a student.

The LED is very close to, and facing the light dependent resistor (LDR). The circuit is taken into a dark room.

The student thought that the LED would switch on. Instead, the LED was found to repeatedly switch on and off.

Explain this behaviour of the LED in this potential divider circuit.

Suggest a possible refinement so that the LED switches on permanently when taken into the dark room.

A beam of -particles is incident on a thin gold foil. Most -particles pass straight through the foil. A few are deflected by gold nuclei.

The diagram shows the path of one -particle which passes close to a gold nucleus N in the foil. The -particle is deflected through an angle of 60° as it travels from A to B.

P marks its position of closest approach to the gold nucleus.

Another -particle in the beam is deflected by the same gold nucleus N through an angle of 30°.

Sketch its path onto the diagram above.

The initial kinetic energy of each -particle is 5.0 MeV.

Show that the magnitude of the initial momentum of each -particle is about 10^–19 kg m s^–1 Take the mass of the -particle to be 6.6 × 10^–27 kg.

Draw two vectors in the spaces below to represent the initial momentum and the final momentum of the -particle.

initial momentum at A

final momentum at B

Draw a vector in the space below to represent the momentum of the nucleus N when the -particle reaches B.

Explain how you determined this momentum.

Use Fig. 19.2 to show that the p.d. across the 50 resistor is 0.50 V.

Calculate the e.m.f. E of the power supply.

The LED emits blue light of wavelength 4.7 × 10^–7 m.

Estimate the number of blue light photons emitted from the LED per second.

number of photons per second =........ s^–1

The light from the LED is incident on a metal of work function 2.3 eV.

Explain, with the help of a calculation, whether or not photoelectrons will be emitted from the surface of the metal.

Hydrogen atoms excited in a discharge tube only emit four different discrete wavelengths of visible photons.

Show that the energy of a photon of wavelength 486 nm is 4.09 × 10^–19 J. (b) (i)

Fig. 5.4 shows some of the energy levels of an electron in a hydrogen atom.

Draw an arrow on Fig. 5.4 to show an electron transition which would cause the emission

of a photon of wavelength 486 nm.

Draw the straight line of best fit on Fig 20.1 and determine the gradient of the line.

gradient =........ V m

Calculate the percentage difference between your value in (ii) and the accepted value of the Planck constant.

Identify the two types of errors shown by the data in Fig. 20.1 and suggest how you could have refined the experiment to reduce or eliminate these errors.

Fig. 20.2 shows a gold-leaf electroscope with a clean zinc plate.

The zinc plate, metal stem and the gold-leaf are given a negative charge by briefly connecting the zinc plate to the negative electrode of a high-voltage supply.

The gold leaf is fully diverged.

The position of the leaf is not affected by intense white light from a table lamp incident on the zinc plate. The gold leaf collapses very quickly when low-intensity ultraviolet radiation from a mercury lamp is incident on the zinc plate.

Explain these observations in terms of photons.

The structure of atoms was deduced in the early 1900s by Rutherford and his co-workers from the scattering of alpha-particles by a very thin sheet of gold.

Rutherford assumed that the scattering of the alpha-particles was due to electrostatic forces. Fig. 23 shows a detector used to record the number N of alpha-particles scattered through an

At = 0°, N was too large to be measured. The table below summarises some of the collected data.

/ °	lg (N)
150	1.5
75	2.3
60	2.7
30	3.9
15	5.1
0	N too large

Show that the number of alpha-particles scattered through 15° is about 4000 times more than those scattered through 150°.

Use the evidence from the table to explain the structure of the atom.

A proton with kinetic energy 0.52 MeV is travelling directly towards a stationary nucleus of cobalt-59 (⁵⁹₂₇Co) in a head-on collision.

Explain what happens to the electric potential energy of the proton-nucleus system.

Calculate the minimum distance R between the proton and cobalt nucleus.

Explain why a high-speed proton is necessary to trigger the nuclear reaction shown above.

Estimate the minimum wavelength λ of the gamma ray photon ().

Fluorine-18 is a positron emitter. Name a medical imaging technique that uses fluorine-18 and state one benefit of the technique.

Describe how the components of a computerised axial tomography (CAT) scanner can produce high-quality images of the internal structures of a patient.

Fig. 6.1 shows a single photomultiplier tube and its internal components. The tube can detect gamma photons in high-energy physics experiments. A single gamma photon incident on the scintillator crystal generates many photons of blue light. These visible light photons travel to the photocathode where they are converted into photoelectrons. The number of electrons is then multiplied in the photomultiplier tube with the help of electrodes called dynodes. A short pulse of electric current is produced at the output end of the photomultiplier tube.

Fig. 6.2 shows a section through the scintillator crystal in air.

The refractive index of the scintillator crystal for visible light is 1.69. The refractive index of air is 1.00. Calculate the critical angle C for this crystal.

Explain why the visible light inside the scintillator crystal follows the path shown in Fig. 6.2.

A high energy gamma photon passing through the scintillator crystal converts some of its energy into visible light photons of mean wavelength 450 nm.

Show that the energy of a single photon of wavelength 450 nm is less than 3 eV.

The photocathode is coated with potassium which has a work function of 2.3 eV. Each emitted photoelectron is accelerated by a potential difference of 100 V between the photocathode and a metal plate, called the first dynode.

Show that the maximum kinetic energy of an emitted electron at the photocathode is very small compared to its kinetic energy of 100 eV at the first dynode.

2000 photoelectrons are released from the photocathode. Each photoelectron has enough energy to release four electrons from the first dynode at the collision. These four electrons are then accelerated to the next dynode where the process is repeated. There are 9 dynodes in the photomultiplier tube. The total number of electrons collected at the anode for each photoelectron is 4⁹.

The pulse of electrons at the anode lasts for a time of 2.5 × 10⁻⁹ s.

Calculate the average current due to this pulse.

Electromagnetic radiation is incident on a negatively charged zinc plate. Electrons are emitted from the surface of the plate when a weak intensity ultraviolet source is used. Electrons are not emitted at all when an intense visible light from a lamp is used.

Explain these observations.

The maximum wavelength of the electromagnetic radiation incident on the surface of a metal which causes electrons to be emitted is 2.9 10⁻⁷ m.

Calculate the maximum kinetic energy of electrons emitted from the surface of the metal when each incident photon has energy of 5.1 eV.

Stars produce energy by nuclear fusion. One particular fusion reaction between two protons (¹₁H) is shown below.

In this reaction 2.2 MeV of energy is released.

Only one of the particles shown in the reaction has binding energy. Determine the binding energy per nucleon of this particle. Explain your answer.

Explain why high temperatures are necessary for fusion reactions to occur in stars.

A gamma photon in a star can spontaneously create an electron-positron pair. Calculate the maximum wavelength of a gamma photon for this creation event.