Question

After how many collisions will be electron be unable to come out of the metal?

• A. 2
• B. 6
• C. 4
• D. 8

Answer 1

The correct option is C 4

Energy of the photon, $E=\frac{hc}{\lambda }=\frac{6.6\times {10}^{-34}\times 3\times {10}^8}{400\times {10}^{-9}}=4.95\times {10}^{-19}J=3.09eV$
After 1st collision energy left, $E_1=0.9\times 3.09=2.78eV$
After 2nd collision energy left $E_2=0.9\times 2.78=2.50eV$
After 3rd collision energy left $E_3=0.9\times 2.50=2.25eV$
After 4th collision energy left $E_3=0.9\times 2.25=2.03eV$ which is less than the work function.

Thus, after 4 collisions the electron will be unable to come out of the metal.