Physics 2: Physical Science & Technology (PHYC10004)
Week 9
Discussion questions
1 (a) A (clean) zinc plate is charged electrostatically. When ultraviolet light strikes the surface, the zinc plate discharges, even though it is on an electrically insulated surface. Explain how this occurs.
(b) Is it possible to charge an uncharged zinc plate by shining UV light on it?
2 In a typical photoelectric cell, as shown below, it appears that the circuit is incomplete, but a current can be observed to flow between the cathode and the anode. Explain how this can occur. (Include in your explanation the role of the battery in the circuit.)
3 One thousand photons uniformly distributed in wavelength between 1100 and 1600 nm exert pressure on a surface they strike. Suppose a prism is used to remove all the photons having wavelengths below 1350 nm. Will the radiation pressure be reduced by (a) less than half, (b) half, or (c) more than half? Explain.
4 Which is true? The minimum frequency required to observe the photo-electric effect is:
(a) The frequency that shakes the electron hard enough to remove it from the atom.
(b) The frequency that provides photons of just sufficient energy to overcome the binding energy of the electron to the surface.
(c) The frequency that provides sufficient amplitude to shake the electron loose.
Problem-solving questions
5
Monochromatic-light is incident on a polished zinc plate that forms part ofa photoelectric measurement apparatus. Electrons are observed to be emitted from the surface of the plate, with maximum kinetic energy of 1.13 eV. The work function for zinc is 4.24 eV.
a) Calculate the energy (in eV) of photons in the incident light
b) Explain what is meant by the term work function.
c) What is the minimum kinetic energy of electrons which are emitted?
d) If the wavelength of the incident light was doubled, would you still expect to see electrons emitted from the plate? Give reasons for your answer.
e) Calculate the wavelength of the light.
f) If the intensity of the light was increased by 50%, by what fraction would the maximum velocity of the electrons increase?
6
A small laser is emitting light of wavelength 550 nm. It has a power of 1 mW. Calculate how many photons leave the laser every second.
7
Consider a planet orbiting a star. Most astronomical bodies can be considered ‘black bodies’.
DATA • radius of planet = 6.4 × 106 m
• solar radiation striking the planet = 1500 J m–2. s–1
• Constant in Stefan’s Law (σ) = 5.7 × 10–8 W m–2 K–4
(i) Show that the total energy reaching the planet in one second is 1.93 × 1017 J.
(ii) Now assume that the planet is in thermal equilibrium, and it radiates this amount of energy into space every second. You can assume that the planet is a ‘black body’, and that it radiates uniformly all over its surface.
Calculate the temperature of the planet in degrees Celsius.
(iii) Use your answer to part (ii) to estimate the peak wavelength (λMAX) radiated by the planet.
8 (mini-challenge question)
Consider the problem of the distribution of radiation in blackbodies. Note that as T increases, the wavelength λmax at which u(λ, T) reaches a maximum shifts toward shorter wavelengths.
a) Show that there is a general relationship between temperature and λmax stating that Tλmax =constant.
b) Given that there exists a solution for the function x = 5(1 — e-x) when x = 4.965, find a numerical value for this constant
(Hint: start with Planck’s relation and note that the slope of u(λ, T) is zero when λ = λmax.)
Past examination questions
9 The electromagnetic spectrum of the sun is often cited as a classic example of a blackbody radiator of characteristic temperature approximately 5500 K. In comparison, a glowing candle (also a blackbody radiator) is characterised by a much lower temperature, typically estimated to be 800 K.
a) With aid of a diagram, compare the blackbody spectra of the sun and a candle. Label all your axes.
b) Use the information above, together with the measured solar diameter of 2.4 × 109 m, to calculate the radiative power output of the sun.
10 Australian freeway lighting is generally provided by sodium discharge lamps. These emit a yellow light of wavelength 589 nm. Each lamp typically consumes 750 W of electricity.
a) Calculate the energy of a single photon from such a lamp.
b) How many photons are emitted each second, assuming the lamp is 100% efficient.