Question

A light of wavelength $3540 \, \mathring{A}$ falls on a metal having work function of $2.5 \,eV$. The ejected electron collides with another target metal inelastically and its total kinetic energy is utilized to raise the temperature of target metal. The mass of target metal is $10^{-3} \,kg$ and its specific heat is $160\, J \,kg ^{-1}{ }^{\circ} \,C ^{-1}$. If $10^{18}$ electrons are ejected per second, then find the rate of raise of temperature $\left(\right.$ in $\left.{ }^{\circ} \,C / s \right)$ of the metal. (Assume there is no loss of energy of ejected electron by any other process, all the electron are reaching the target metal with maximum kinetic energy and $h c=12400 eV \, \mathring{A}$ )

Answer 1

Energy of photon $=\frac{h c}{\lambda}=\frac{12400}{3540} eV \approx 3.5 \,eV$
Thus, $K E_{\max }$ of ejected electron $=1 \,eV$
Thus, energy lost per electron
$=1 \, eV =1 \times 1.6 \times 10^{-19} J$
Total energy gained by target metal per second
$=1.6 \times 10^{-19} \times 10^{18} J =0.16 \, J$
Thus, $0.16=m s \frac{d T}{d t} $
$\Rightarrow \cdot \frac{d T}{d t}={\frac{0.16}{10^{-3} \times 160}}^{\circ} C / s$