Science > Physics > Photoelectric Effect > Numerical Problems on Photoelectric Effect
In this article, we shall study to calculate, Energy of incident photon, threshold wavelength and threshold frequency of metal.
Example – 01:
The energy of a photon is 2.59 eV. Find its frequency and wavelength.
Given: Energy of photon = E = 2.59 eV = 2.59 x 1.6 x 10-19 J, speed of light = c = 3 x 108 m/s, Planck’s constant = h = 6.63 x 10-34 Js
To Find: Frequency of photon = ν =? Wavelength = λ = ?
Solution:
We have E = h ν
∴ ν = E/h = (2.59 x 1.6 x 10-19) / (6.63 x 10-34) = 6.244 x 1014 Hz
Now c = ν λ
∴ λ = c/ν = (3 x 108) / ( 6.244 x 1014) = 4.805 x 10-7 m
∴ λ = 4805 x 10-10 m = 4805 Å
Ans: The frequency of photon is 6.244 x 1014 Hz and its wavelength is 4805 Å
Example – 02:
The energy of a photon is 1.0 x 10-8 J. Find its frequency and wavelength.
Given: Energy of photon = E = 1.0 x 10-18 J, speed of light = c = 3 x 108 m/s, Planck’s constant = h = 6.63 x 10-34 Js
To Find: Frequency of photon = ν =? Wavelength = λ = ?
Solution:
We have E = h ν
∴ ν = E/h = (1.0 x 10-18) / (6.63 x 10-34) = 1.508 x 1015 Hz
Now c = ν λ
∴ λ = c/ν = (3 x 108) / ( 1.508 x 1015) = 1.989 x 10-7 m
∴ λ = 1989 x 10-10 m = 1989 Å
Ans: The frequency of photon is 1.508 x 1014 Hz and its wavelength is 1989 Å
Example – 03:
The energy of a photon is 300 eV. Find its wavelength.
Given: Energy of photon = E = 300 eV = 300 x 1.6 x 10-19 J, speed of light = c = 3 x 108 m/s, Planck’s constant = h = 6.63 x 10-34 Js
To Find: Wavelength = λ =?
Solution:
We have E = h ν = hc/λ
∴ λ = hc / E = (6.63 x 10-34)(3 x 108)/(300 x 1.6 x 10-19) = 4.144 x 10-9 m
∴ λ = 41.44 x 10-10 m = 41.44 Å
Ans: The wavelength of photon is 41.44 Å
Example – 04:
Find the energy of a photon in eV if its wavelength is 10 m
Given: Wavelength of photon = λ = 10 m, speed of light = c = 3 x 108 m/s, Planck’s constant = h = 6.63 x 10-34 Js
To Find: Wavelength = λ =?
Solution:
E = hc/λ = (6.63 x 10-34)(3 x 108)/(10) = 19.89 x 10-27 J
∴ E = (19.89 x 10-27)/(1.6 x 10-19) = 1.243 x 10-7 eV
Ans: The energy of the photon is 1.243 x 10-7 eV
Example – 05:
Find the energy of a photon whose frequency is 5.0 x 1014 Hz
Given: Frequency of photon = ν = 5.0 x 1014 Hz, Planck’s constant = h = 6.63 x 10-34 Js
To Find: Energy of photon = E =?
Solution:
We have E = h ν
∴ E = (6.63 x 10-34) x (5.0 x 1014)= 3.315 x 10-29 J
Ans: The energy of the photon is 3.315 x 10-29 J
Example – 06:
The photoelectric work function of silver is 3.315 eV. Calculate the threshold frequency and threshold wavelength of silver.
Given: Work function of silver = Φ = 3.315 eV = 3.315 x 1.6 x 10-19 J, speed of light = 3 x 108 m/s, Planck’s constant = h = 6.63 x 10-34 Js
To Find: Threshold frequency of silver = νo =? Threshold wavelength of silver = λo = ?
Solution:
We have Φ = h νo
∴ νo = Φ/h = (3.315 x 1.6 x 10-19)/(6.63 x 10-34) = 8 x 1014 Hz
Now c = νo λo
∴ λo = c/νo = (3 x 108)/( 8 x 1014) = 3.750 x 10-7 m
∴ λo= 3750 x 10-10 m = 4805 Å
Ans: The threshold frequency of silver is 8 x 1014 Hz and its threshold wavelength is 3750 Å
Example – 07:
A light of wavelength 4800 Å can just cause photoemission from a metal. What is the photoelectric work function for metal in eV?
Given: Threshold wavelength = λo = 4800 Å = 4800 x 10-10 m, speed of light = c = 3 x 108 m/s, Planck’s constant = h = 6.63 x 10-34 Js
To Find: Work function of silver = Φ =?
Solution:
We have Φ = h νo = hc/λo
∴ Φ = (6.63 x 10-34) x (3 x 108) / (4800 x 10-10) = 4.144 x 10-19 J
∴ Φ = (4.144 x 10-19) / (1.6 x 10-19) = 2.59 eV
Ans: The photoelectric work function of the metal is 2.59 eV
Example – 08:
The photoelectric work function of a metal is 2 eV. Calculate the lowest frequency radiation that will cause photoemission from the surface.
Given: Work function of silver = Φ = 2 eV = 2 x 1.6 x 10-19 J, Planck’s constant = h = 6.63 x 10-34 Js
To Find: Threshold frequency of silver = νo =?
Solution:
We have Φ = h νo
∴ νo = Φ/h = (2 x 1.6 x 10-19)/(6.63 x 10-34) = 4.827 x 1014 Hz
Ans: The threshold frequency of metal is 4.827 x 1014.
Example – 09:
The photoelectric work function of platinum is 6.3 eV and the longest wavelength that can eject photoelectron from platinum is 1972 Å. Calculate the Planck’s constant.
Given: Work function of platinum = Φ = 6.3 eV =6.3 x 1.6 x 10-19 J, Threshold wavelength of silver = 1972 Å = 1972 x 10-10 m, speed of light = c = 3 x 108 m/s,
To Find: Planck’s constant = h =?
Solution:
We have Φ = h νo = hc/λo
∴ h = Φλo/c = (6.3 x 1.6 x 10-19) x (1972 x 10-10) / (3 x 108) = 6.625 x 10-34 Js
Ans: The value of Planck’s constant is 6.625 x 10-34 Js
Example – 10:
The photoelectric work function of metal is 1.32 eV. Calculate the longest wavelength that can cause photoelectric emission from the metal surface.
Given: Work function of silver = Φ = 1.32 eV = 1.32 x 1.6 x 10-19 J, speed of light = c = 3 x 108 m/s, Planck’s constant = h = 6.63 x 10-34 Js
To Find: Threshold wavelength of metal = λo =?
Solution:
We have Φ = h νo = hc/λo
∴ λo = hc/Φ =(6.63 x 10-34) x (3 x 108) / (1.32 x 1.6 x 10-19) = 9.418 x 10-7 m
∴ λo= 9418 x 10-10 m = 9418 Å
Ans: The threshold wavelength is 9418 Å
Example – 11:
The photoelectric work function of metal is 5 eV. Calculate the threshold frequency for the metal. If a light of wavelength 4000 Å is incident on this metal surface, will photoelectron will be ejected?
Given: Work function of silver = Φ = 5 eV = 5 x 1.6 x 10-19 J, speed of light = c = 3 x 108 m/s, Planck’s constant = h = 6.63 x 10-34 Js, wavelength of incident light = λ = 4000 Å = 4000 x 10-10 m
To Find: Threshold wavelength of metal = λo =?
Solution:
We have Φ = h νo
∴ νo = Φ/h = (5 x 1.6 x 10-19)/(6.63 x 10-34) = 1.2 x 1015 Hz
Now c = ν λ
∴ ν = c/λ = (3 x 108) / ( 4000 x 10-10) = 7.5 x 1014 Hz
The frequency of incident light is less than the threshold frequency.
No photoelectrons will be emitted from the metal surface.
Ans: The threshold frequency is 1.2 x 1015 Hz and no photoelectron will be emitted.
Example – 12:
The photoelectric work function of a metal is 2.4 eV. Calculate the incident frequency, the threshold frequency for the metal. If a light of wavelength 6800 Å is incident on this metal surface, will photoelectron will be ejected?
Given: Work function of silver = Φ = 2.4 eV= 2.4 x 1.6 x 10-19 J, speed of light = c = 3 x 108 m/s, Planck’s constant = h = 6.63 x 10-34 Js, wavelength of incident light = λ = 6800 Å = 6800 x 10-10 m
To Find: Threshold wavelength of metal = λo =?
Solution:
We have Φ = h νo
∴ νo = Φ/h = (2.4 x 1.6 x 10-19)/(6.63 x 10-34) = 5.79 x 1014 Hz
Now c = ν λ
∴ ν = c/λ = (3 x 108) / ( 6800 x 10-10) = 4.41 x 1014 Hz
The frequency of incident light is less than the threshold frequency.
No photoelectrons will be emitted from the metal surface.
Ans: The incident frequency is 4.41 x 1014 Hz and the threshold frequency is 5.79 x 1014 Hz, and no photoelectron will be ejected.
Example – 13:
The photoelectric work function of a metal is 3 eV. Calculate the threshold frequency for the metal. If light of wavelength 6000 Å is incident on this metal surface, will photoelectron will be ejected?
Given: Work function of silver = Φ = 3 eV = 3 x 1.6 x 10-19 J, speed of light = 3 x 108 m/s, planck’s constant = h = 6.63 x 10-34 Js, wavelength of incident light = λ = 6000 Å = 6000 x 10-10 m
To Find: Threshold wavelength of metal = λo =?
Solution:
We have Φ = h νo
∴ νo = Φ/h = (3 x 1.6 x 10-19)/(6.63 x 10-34) = 7.24 x 1014 Hz
Now c = ν λ
∴ ν = c/λ = (3 x 108)/( 6000 x 10-10) = 5 x 1014 Hz
The frequency of incident light is less than the threshold frequency.
No photoelectrons will be emitted from the metal surface.
Ans: The threshold frequency is 7.24 x 1014 Hz,
and no photoelectron will be ejected.
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