Question

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:

• A. All have the same K.E.=hν−hν$_0​$
• B. Maximum K.E.=hν−hν$_0$​
• C. Maximum K.E.=hν
• D. K.E.=hν$_0$​

Answer 1

The Correct Option is B

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:

1. Incorrect: Not all electrons have the same KE
2. Correct: Electrons have a distribution, with max KE = \( h\nu - h\nu_0 \)
3. Incorrect: Max KE is \( h\nu - h\nu_0 \), not \( h\nu \)
4. Incorrect: KE depends on photon energy, not just work function

Correct Answer: Option 2

Answer 2

In the photoelectric effect, electrons are ejected with a range of kinetic energies. 
The maximum kinetic energy of an electron is given by:
K. E_max = hν −hν₀ 
where hν is the energy of the incident photon and hν0 is the work function. 
Not all electrons have the same energy, as some may lose energy due to collisions within the metal, leading to a distribution of kinetic energies