JEE PHYSICS MCQ: DUAL NATURE OF RADIATION AND MATTER

The constant $A$ in the Richardson-Dushman equation for tungsten is $60 \times 10^4 \mathrm{~A} \mathrm{~m}^{-2} \mathrm{~K}^{-2}$. The work function of tungsten is $4.5 \mathrm{~eV}$. A tungsten cathode having a surface area $2.0 \times 10^{-5} \mathrm{~m}^2$ is heated by a $24 \mathrm{~W}$ electric heater. In steady state, the heat radiated by the cathode equals the energy input by the heater and the temperature becomes constant. Assuming that the cathode radiates like a blackbody, calculate the saturation current due to thermions. Take Stefan constant $=6 \times 10^{-8} \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-4}$. Assume that the thermions take only a small fraction of the heat supplied.