Question

Work function of lithium and copper are respectively $2.3$ and $4.0 \,eV$. Which one of the metals will be useful for the photoelectric cell working with visible light ? $ (h=6.6\times {{10}^{-34}}J-s,\,c=3\times {{10}^{8}}m/s) $

• A. Lithium
• B. Copper
• C. Both
• D. None

Answer 1

Answer: (A)

The approximate range of visible spectrum is $400$ to $700 \,nm$.
The minimum energy required for the emission of photoelectrons from a metal is called the work function of that metal.
$ W=\frac{hc}{\lambda } $
$ \Rightarrow $ $ \lambda =\frac{hc}{W}$
$=\frac{6.6\times {{10}^{-34}}\times 3\times {{10}^{8}}}{2.3\times 1.6\times {{10}^{-19}}} $
$ =5.38\times {{10}^{-7}}m = 538\, nm $ (for lithium)
For copper $ \lambda =\frac{hc}{W}$
$=\frac{6.6\times {{10}^{-34}}\times 3\times {{10}^{8}}}{4\times 1.6\times {{10}^{-19}}}=309\,nm $
Since, wavelength range of visible spectrum is $400 \,nm$ to $700\, nm$,
have only lithium lies in this range. Hence, lithium is useful.