Question

A light of wavelength $\lambda$ is incident on a metal sheet of work function $\varphi =2eV$. The wavelength $\lambda$ varies with time as $\lambda =3000+40t$, where $\lambda$ is in $A^{\circ }$ and t is in second. The power incident on metal sheet is constant at 100 W. This signal is switched on and off for time intervals of 2 minutes and 1 minute respectively. Each time the signal is switched on, the $\lambda$ start from initial value of $3000A^{\circ }$. The metal plate is grounded and electron clouding is negligible. The efficiency of photoemission is 1% $(hc=12400eV{A}^{\circ }).$

The total number of photoelectrons ejected in one hour is ​​​​​​​

• A. $3.71\times {10}^{20}$
• B. $3.71\times {10}^{21}$
• C. $3.71\times {10}^{22}$
• D. $3.71\times {10}^{23}$

Answer 1

The correct option is B $3.71\times {10}^{21}$

Rate of photo emission at time t
$\frac{dN}{dt}=\frac{1}{100}\times \frac{100}{19840\times {10}^{-19}}[3000+40t]$
$N=\frac{1}{19840\times {10}^{-19}}[3000t+20t^2{]}_0^{80}$
$N=18.55\times {10}^{19}=1.855\times {10}^{20}$
This is the number of photoelectron ejected in 1 blinking.
In 1 hr, total number of photoelectron ejected is
$=1.855\times {10}^{20}\times 20=3.71\times {10}^{21}$