Problems on Photoelectricity: UNIZOR.COM - Physics4Teens - Waves - Photoelectricity

Notes to a video lecture on http://www.unizor.com

Problems on Photoelectricity

Problem A

Energy needed to tear a particular electron from the attraction of its nucleus is called binding energy of this electron.
Knowing it, we can calculate the minimum frequency of incident light to initiate photoemission of this type of an electron.

Express the minimum frequency of incident light f_min as a function of a binding energy of an electron E_binding.
Find the corresponding period of oscillations and the wave length.
Assume, the medium of light propagation is vacuum.

Solution

Energy of a single photon of an incident light h·f_min should be, at least, equal to E_binding.
Therefore,
E_binding = h·f_min
where h is the Planck's constant.
From this
f_min = E_binding/h
Angular frequency
ω = 2π·f = 2π·E_binding/h
Period of oscillations is inverse of a frequency
τ = 1/f = h/E_binding
The wave length λ depends of speed of light c and a period τ:
λ = c·τ
Therefore,
λ = c·h/E_binding


Problem B

Using the results of Problem A above, calculate the minimum frequency of light required to start photoemission from a plate made of gold.
Also find the corresponding wave length of this light.
Perform calculations to three decimal places.
Consider the value of binding energy of a particular electron in gold to be
E_binding=5.17eV (electron-volt)
and the value of Planck constant
h=6.62607015·10⁻³⁴m²·kg/s

NOTE about electron-volt (eV) as a unit of energy and its relation with SI unit of energy joule (J).
1eV is an amount of kinetic energy gained by a single electron moving within an electrostatic field from point A to point B with the difference in electric potential between these points equal to 1V (volt).
Because the charge of an electron in coulombs (C) is 1.602176634·10⁻¹⁹C,
and 1V·1C=1J,
1 eV = 1.602176634·10⁻¹⁹J.

Solution

E_binding = 5.17eV =
= 5.17·1.602·10⁻¹⁹J =
= 8.282·10⁻¹⁹J
Light frequency, as described above is related to the energy of its photons, it can be calculated from the formula
E_binding = h·f_min
where h is the Planck's constant.
Therefore,
f_min = E_binding/h =
= 8.282·10⁻¹⁹J /
/(6.626·10⁻³⁴m²·kg/s) =
= 1.250·10¹⁵ J·s/(m²·kg)
Notice,
J = N·m = kg·m²/s²
Therefore, the units of this result are
J·s/(m²·kg) = N·m·s/(m²·kg) =
= kg·m²·s/(m²·kg·s²) = 1/s
which is the right units for frequency (number of oscillations per second).
So, we express the frequency in usual units 1/s:
f_min = 1.250·10¹⁵ 1/s

Wave length calculation is based on the speed of light, approximately, 3·10⁸ m/s.
λ = c·τ = c/f =
= 3·10⁸/(1.250·10¹⁵) m·s/s =
= 2.4·10⁻⁷m = 240nm
This wavelength is below the visible spectrum from about 400 to about 700 nanometers and belongs to ultraviolet segment.