Question

The work function of a photoelectric material is 4.0 eV. What is the threshold wavelength?

• A. 374 nm
• B. 310 nm
• C. 352 nm
• D. 398 nm

Answer 1

The correct option is B

310 nm

The minimum energy carried by a photon $E_{min}=h{v}_{min},$ that ejects a photoelectron off a metal surface is defined as the work function for the metal. The frequency corresponding to this minimum energy is called the threshold frequency, or ${\nu }_{min}\equiv {\nu }_{threshold}.$

$\therefore E_{min}=W$

$\Rightarrow h{\nu }_{threshold}$=$\frac{hc}{{\lambda }_{threshold}}$ W=4.0 eV ($\because$ the wavelength and frequency are related as $\nu \lambda =c$)

$\Rightarrow {\lambda }_{threshold}$=$\frac{hc}{W}$=$\frac{6.626\times {10}^{-34}Js\times 3\times {10}^{8}m/s}{4.0\times 1.603\times {10}^{-19}Js}$ $\approx 3.1\times {10}^{-7}m=310nm$
The correct choice is (b)!