Statement-1: When ultraviolet light is incident on a photocell, its stopping potential is $\mathrm{V}_{0}$ and the maximum kinetic energy of the photoelectrons is $\mathrm{K}_{\max}$. When the ultraviolet light is replaced by X rays, both $\mathrm{V}_{0}$ and $\mathrm{K}_{\text{max}}$ increase. Statement-2: Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.

(D) Statement-1 is true, Statement-2 is false.

(A) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

(B) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

(C) Statement-1 is false, Statement-2 is true.

JEE Main · 2010 · 11 Apr 2010 · Offline · Modern Physics

Statement-1: When ultraviolet light is incident on a photocell, its stopping potential is

V_{0}

and the maximum kinetic energy of the photoelectrons is

K_{m a x}

. When the ultraviolet light is replaced by X rays, both

V_{0}

and

K_{max}

increase.

Statement-2: Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.

(A)Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.
(B)Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.
(C)Statement-1 is false, Statement-2 is true.
(D)Statement-1 is true, Statement-2 is false.✓ Correct

Answer: (D)

Solution

Replacing ultraviolet light by X-rays raises the photon frequency sharply. Since the maximum kinetic energy of the ejected electrons is

K_{m a x} = h ν - ϕ

and the stopping potential is

V_{0} = K_{m a x} / e

, both rise when the frequency rises, so Statement-1 is true. Statement-2 gives the wrong reason for the spread of electron energies: with monochromatic light every photon has one single frequency, so the range of emitted speeds cannot come from a range of frequencies. It arises instead because electrons start from different depths in the metal and lose differing amounts of energy escaping. Statement-2 is therefore false.

JEE Main · 2010 · 11 Apr 2010 · Offline · Single correct option

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JEE Main · 2010 · 11 Apr 2010 · Offline · Modern Physics

Solution

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