Question:
The threshold frequency for a certain metal is \(3.3×10^{14} Hz\). If light of frequency \(8.2×10^{14} Hz\) is incident on the metal,predict the cut-off voltage for the photoelectric emission.
The threshold frequency for a certain metal is \(3.3×10^{14} Hz\). If light of frequency \(8.2×10^{14} Hz\) is incident on the metal,predict the cut-off voltage for the photoelectric emission.
Updated On: Sep 29, 2023
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Solution and Explanation
The correct answer is: 2.0292V.
Threshold frequency of the metal, \(v_0=3.3×10^{14}Hz.\)
Frequency of light incident on the metal, \(v=8.2×10^{14}Hz\)
Charge on an electron, \(e=1.6×10^{−19}C\)
Planck’s constant, \(h=6.626×10^{−34}Js\)
Cut-off voltage for the photoelectric emission from the metal\(=V_0\)
The equation for the cut-off energy is given as:
\(eV_0=h(v-v_0)\)
\(v_0=\frac{h(v-v_0)}{e}\)
\(=\frac{6.62×10^{-34}×(8.2×10^{14}-3.3×10^{14})}{1.6×10^{-19}}=2.0292V\)
Therefore,the cut-off voltage for the photoelectric emission is 2.0292V.
Threshold frequency of the metal, \(v_0=3.3×10^{14}Hz.\)
Frequency of light incident on the metal, \(v=8.2×10^{14}Hz\)
Charge on an electron, \(e=1.6×10^{−19}C\)
Planck’s constant, \(h=6.626×10^{−34}Js\)
Cut-off voltage for the photoelectric emission from the metal\(=V_0\)
The equation for the cut-off energy is given as:
\(eV_0=h(v-v_0)\)
\(v_0=\frac{h(v-v_0)}{e}\)
\(=\frac{6.62×10^{-34}×(8.2×10^{14}-3.3×10^{14})}{1.6×10^{-19}}=2.0292V\)
Therefore,the cut-off voltage for the photoelectric emission is 2.0292V.
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Concepts Used:
Photoelectric Effect
When light shines on a metal, electrons can be ejected from the surface of the metal in a phenomenon known as the photoelectric effect. This process is also often referred to as photoemission, and the electrons that are ejected from the metal are called photoelectrons.
Photoelectric Effect Formula:
According to Einstein’s explanation of the photoelectric effect :
The energy of photon = energy needed to remove an electron + kinetic energy of the emitted electron
i.e. hν = W + E
Where,
- h is Planck’s constant.
- ν is the frequency of the incident photon.
- W is a work function.
- E is the maximum kinetic energy of ejected electrons: 1/2 mv².
Laws of Photoelectric Effect:
- The photoelectric current is in direct proportion to the intensity of light, for a light of any given frequency; (γ > γ Th).
- There exists a certain minimum (energy) frequency for a given material, called threshold frequency, below which the discharge of photoelectrons stops completely, irrespective of how high the intensity of incident light is.
- The maximum kinetic energy of the photoelectrons increases with the increase in the frequency (provided frequency γ > γ Th exceeds the threshold limit) of the incident light. The maximum kinetic energy is free from the intensity of light.
- The process of photo-emission is an instantaneous process.