Question

Two statements are given — one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer from the options below:

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(C) Assertion (A) is true, but Reason (R) is false.
(D) Both Assertion (A) and Reason (R) are false.

Assertion (A): In process of photoelectric emission using a monochromatic light, all emitted electrons do not have the same kinetic energy.

Reason (R): If radiation falling on a photosensitive surface consists of different wavelengths, the energy of emitted photoelectrons by absorbing photons of different wavelengths, shall be different.

• A. A
• B. B
• C. C
• D. D

Hint:

Monochromatic light still gives electrons of different energies because electrons lose energy inside the metal. The Reason talks about different wavelengths, which is a different cause, so it does not explain the Assertion.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In the photoelectric effect a photon of energy \(h\nu\) is absorbed by one electron. The electron uses \(\phi\) (the work function) to leave the metal and keeps the rest as kinetic energy.
Einstein equation: \(K_{max} = h\nu - \phi\). This is the largest kinetic energy, for electrons at the surface.

Step 2: Check the Assertion (A):
With monochromatic light every photon has the same energy \(h\nu\).
Electrons sit at different depths. A deeper electron loses some energy in collisions before it leaves the metal.
So the emitted electrons have kinetic energies from nearly zero up to \(K_{max}\). They do not all have the same energy. (A) is TRUE.

Step 3: Check the Reason (R):
Photon energy is \(E = hc/\lambda\). Light of different wavelengths has photons of different energies.
So electrons absorbing these photons come out with different kinetic energies. (R) is a true statement.

Step 4: Decide whether R explains A:
The Assertion is about light of ONE wavelength. The Reason talks about light of SEVERAL wavelengths.
The spread of energies in a single-wavelength beam comes from energy loss inside the metal, not from a mixture of wavelengths.
So (R) does not explain (A). Both are true, but (R) is not the correct explanation.

Step 5: Why the other options are wrong:
Option (A) says R explains A. It does not, as shown above.
Option (C) says R is false. R is a correct statement.
Option (D) says both are false. Both are true.

Final Answer:
Both statements are true but the Reason does not explain the Assertion. This is option (B). \[ \boxed{\text{(B)}} \]