When a photon of energy hν falls on a photosensitive metallic surface (work function hν0), electrons are emitted from the metallic surface. It is possible to say that:
- All have the same K.E.=hν−hν$_0$
- Maximum K.E.=hν−hν$_0$
- Maximum K.E.=hν
- K.E.=hν$_0$
The Correct Option is B
Approach Solution - 1
In the photoelectric effect, when a photon of energy \( h\nu \) strikes a photosensitive metallic surface with a work function \( h\nu_0 \), electrons can be emitted. The energy of the incoming photon is used to overcome the work function of the metal; any excess energy is converted into the kinetic energy of the emitted electron.
The energy conservation equation for this process can be written as:
\[ h\nu = h\nu_0 + KE_{\text{max}} \]
where \( KE_{\text{max}} \) represents the maximum kinetic energy of the emitted electrons.
By rearranging the equation, we find:
\[ KE_{\text{max}} = h\nu - h\nu_0 \]
This shows that the maximum kinetic energy of the emitted electrons is equal to the energy of the photon minus the work function of the material.
Therefore, the correct statement from the options provided is: Maximum K.E.=h\nu−h\nu_0.
Approach Solution -2
Photoelectric Effect Solution:
Given:
- Photon energy = \( h\nu \)
- Work function = \( h\nu_0 \)
Key Concepts:
- Einstein's photoelectric equation: \( KE_{max} = h\nu - h\nu_0 \)
- Electrons have varying kinetic energies due to different depths in the metal
- Only the most energetic electrons (surface electrons) have \( KE = h\nu - h\nu_0 \)
Option Analysis:
- Incorrect: Not all electrons have the same KE
- Correct: Electrons have a distribution, with max KE = \( h\nu - h\nu_0 \)
- Incorrect: Max KE is \( h\nu - h\nu_0 \), not \( h\nu \)
- Incorrect: KE depends on photon energy, not just work function
Correct Answer: Option 2
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