Calculate wavelength of incident light when a monochromatic light is incident on a surface of metal with threshold frequency 3.5×10^14 and kinetic energy 1.65
Answers
The stopping potential refers to the potential difference required to stop an electron emitted from a metal after it is illuminated by the light. This potential difference is equal to the kinetic energy with which electron leaves the metal:
K = hf - phi .
This is called photoelectric equation. Here, h is the Plank's constant, f is the frequency of the incident light and phi is the work function of the metal. The work function is related to the threshold frequency of the incident light: phi = hf_0 , where f_0 is the minimum frequency for which any electrons will be emitted.
The frequency of light can be expressed through its wavelength lambda as
f = c/lambda , where c is the speed of light.
In the given problem, the stopping potential for the light with wavelength lambda
is 3V. The photoelectric equation becomes
3V =(hc)/lambda - phi
The stopping potential for the light with wavelength 2lambda is V:
V = (hc)/(2lambda) - phi
These two equations can be solved together for the work function. Multiplying the second equation by -2 and adding it to the first equation results in
V = phi
The work function equals phi = (hc)/lambda_0=V , where lambda_0 is the threshold wavelength. Combining this with second of the photoelectric equations, we get
(hc)/lambda_0 = (hc)/(2lambda) - (hc)/lambda_0
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