The electric field at a point associated with a light wave is given by
E = 200[sin(6 × 1015)t + sin(9 × 1015)t] Vm–1
Given : h = 4.14 × 10–15 eVs
If this light falls on a metal surface having a work function of 2.50 eV, the maximum kinetic energy of the photoelectrons will be
E = 200[sin(6 × 1015)t + sin(9 × 1015)t] Vm–1
Given : h = 4.14 × 10–15 eVs
If this light falls on a metal surface having a work function of 2.50 eV, the maximum kinetic energy of the photoelectrons will be
- 1.90 eV
- 3.27 eV
- 3.60 eV
- 3.42 eV
The Correct Option is A
Solution and Explanation
The correct answer is (D) : 3.42 eV
Frequency of EM waves
\(= \frac{6}{2π} × 10^{15}\)
and
\(\frac{9}{2π} × 10^{15}\)
Energy of one photon of these waves
\(=(4.14 × 10^{-15} × \frac{6}{2π} × 10^{15})eV\)
and
\((4.14 × 10^{-15} × \frac{9}{2π} ×10^{15})eV\)
3.95 eV and 5.93 eV
⇒ Energy of maximum energetic electrons
= 5.93 – 2.50
= 3.43 eV
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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.