Question

The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately:

• A. 540 nm
• B. 400 nm
• C. 310 nm
• D. 220 nm

Answer 1

The correct option is C 310 nm

If ${\lambda }_0$ be the threshold wavelength and $\lambda$ be the wavelength of incident light, the condition for photoelectron emission is $\lambda <{\lambda }_0$

Thus, threshold wavelength is the longest wavelength for photoelectron emission.

So, work function: $W=\frac{hc}{{\lambda }_0}$

or, ${\lambda }_0=\frac{hc}{W}=\frac{(6.62\times {10}^{-34})(3\times {10}^8)}{4\times 1.6\times {10}^{-19}}=3.10\times {10}^{-7}m=310\times {10}^{-9}m=310nm$