Problem

Two metallic plates

A

and

B

each of area

5 \times 10^{-4} \text{ m}^2

, are placed parallel to each other at a separation of

1 \text{ cm}

. Plate

B

carries a positive charge of

33.7 \times 10^{-12} \text{ C}

. A monochromatic beam of light, with photons of energy

5 \text{ eV}

each, starts falling on plate

A

t = 0

so that

10^{16}

photons fall on it per square metre per second. Assume that one photoelectron is emitted for every

10^6

incident photons. Also assume that all the emitted photoelectrons are collected by plate

B

and the work-function of plate

A

remains constant at the value

2 \text{ eV}

. Determine (JEE 2002) Neglect the time taken by the photoelectron to reach plate

B

. (Take,

\epsilon_0 = 8.85 \times 10^{-12} \text{ C}^2/\text{N}\cdot\text{m}^2

). (a) the number of photoelectrons emitted upto

t = 10 \text{ s}

, (b) the magnitude of the electric field between the plates

A

and

B

t = 10 \text{ s}

and (c) the kinetic energy of the most energetic photoelectrons emitted at

t = 10 \text{ s}

when it reaches plate

B