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NCEA Level 3 Physics Problems - Photoelectric Effect
Acceleration due to gravity,g = 9.81 Nkg-1
Speed of light = 3.0 x 108ms-1
Planck's constant = 6.6 x 10-34Js
Mass of electron = 9.1 x 10-31kg
Electronic charge = 1.6 x 10-19C
(1) When light is incident in a metal plate electrons are emitted only when the frequency of the light exceeds a certain
value. How has this been explained?
The maximum kinetic energy of the electrons emitted from a metallic surface is 1.6 x 10 -19J when the frequency of
the incident radiation is 7.5 x 1014 Hz. Calculate the minimum frequency for which electrons will be emitted.
(2) What do you understand by the quantum theory? Describe the evidence provided by experiments on the
photoelectric effect in favour of this theory.
Calculate the energy, in joules, of the photons associated with light of wavelength 3.0 x 10 -7m.
(3) When light of wavelength 5.0 x 10-7m falls on a surface it ejects photoelectrons with a maximum velocity of
6.0 x 105ms-1.
Calculate; (a) the work function in electron-volts
(b) the threshold frequency for the surface.
(4) (a) If a surface has a work function of 3.0 eV, find the longest wavelength light which will cause the emission of
photoelectrons from it.
(b) What is the maximum velocity of photoelectrons liberated from a surface having a work function of 4.0 eV by
ultra-violet radiation of wavelength 2.0 x 10-7m.
(5) In an experiment on the photoelectric effect using radiation of wavelength 4.00 x 10-7m the maximum electron
energy observed was 1.40 x 10-19 J. With a wavelength 3.00 x 10-7m the maximum energy was 3.06 x 10-19J.
Derive a value for Planck's constant. Give one other physical phenomenon involving Planck's constant.
(6) Write down Einstein's equation for photoelectric emission. Explain briefly the meaning of the terms in the equation
and discuss its significance.
Describe briefly how Einstein's equation may be verified experimentally.
An effective point source emits monochromatic light of wavelength 4500 Angstroms at a rate of 0.11 watt. How
many photons leave the source per second?
Light from the source is emitted uniformly in all directions and falls normally on the cathode of area 3.14 cm2 of a
photocell at a distance of 50 cm from the source. Calculate the photoelectric current, assuming 10 % of the photons
incident on the cathode liberate electrons. (1 Angstrom = 10 -10m)
(7) Describe and explain one experiment in which light exhibits a wave-like character and one experiment that
illustrates the existence of photons.
Light of frequency 5.0 x 1014Hz liberates electrons with energy 2.31 x 10-19J from a certain metallic surface. What
is the wavelength of ultra-violet light which liberates electrons of energy 8.93 x 10 -19J from the same surface?
(8) For caesium the work function is 1.35 eV.
(a) what is the longest wavelength that can cause photoelectric emission from a caesium surface?
(b) What is the minimum velocity with which photoelectrons will be emitted from a caesium surface illuminated
with light of wavelength 4000 Angstroms?
(c) What potential difference will just prevent a current passing through a caesium photocell illuminated with light
of wavelength 4000 Angstroms? (1 Angstrom = 10 -10m)
Atomic and Nuclear Physics
(9) When the light received from a star is examined, each line in the spectrum of a particular element in the star is
seen at a wavelength different from that of the same element when viewed in the laboratory. Most galaxies and
some stars are “red-shifted”. That is, their spectral lines appear to be at longer wavelengths. A few of the nearer
galaxies are “violet-shifted” so that their spectral lines appear to be at shorter wavelengths.
(a) State what “violet-shifted” tells us about the motion of the galaxies.
The mean frequency of a sodium line as measured in the laboratory is 5.091 x 10 14Hz. The same line in the light
from a particular star has a frequency of 5.089 x 10 14Hz when viewed from Earth.
(b) State whether the star is moving towards or away from Earth.
(c) Calculate the velocity of the star with respect to Earth. (Ignore relativistic effects)
(d) Calculate the wavelength of sodium light which has a frequency of 5.091 x 10 14Hz.
(e) Calculate the energy of a photon of sodium light.
A double star consists of two stars that are so close together that they appear as a single star. The two stars orbit
about their common center of mass. The overall movement of a particular double star in our own galaxy is such
that when one of the pair is moving towards an observer on Earth, the other is moving away.
One of the stars is “dead” and is no longer producing light, although it still has significant mass.
(f) Describe and explain the effect of the movement of the still visible star on the appearance of its spectrum.
(g) If the mass of the invisible star is more than three times the mass of the Sun, what is it likely to be?
(10) (a) A laser, which produces a beam of parallel, coherent light with a wavelength  = 5.5 x 10-7m, has an optical
power output of 1.0 x 10-3W.
(i)
Explain what is meant by the term coherent.
(ii)
Show that the energy of each photon produced by the laser is 3.6 x 10-19J.
(iii)
How many photons does the laser emit per second? (1 W = 1 Js -1)
(b) In the Bohr model for the hydrogen atom, the angular momentum of the electron is given as L = nh/2
(i)
What do the symbols n and h stand for?
Bohr's theory postulates that the angular momentum of an electron is quantised.
(ii)
What do you understand by the term quantised?
(iii)
Explain why an electron cannot simply move in a circular orbit, as in Rutherford's original model.
The diagram below shows a simplified arrangement to demonstrate the photoelectric effect. Associated with this
phenomenon is the equation Ek = hf - where Ek is the kinetic energy of any released electrons and  is the work
function of the metal being used.
G
- +
V
(c) Explain why, with a particular metal, a weak blue light will liberate electrons but an intense red light will
not.
(d) Why is the small voltage from the cell helpful in the arrangement shown above?
(e) A particular metal emits photoelectrons with a maximum kinetic energy of 8.0 x 10 -20J when illuminated by
light of wavelength 450nm. What is the work function of the metal? What is the minimum frequency of light
that will cause photo-emission of electrons for this particular metal?