Question

The work function of the metal is

• A. 1.45 eV
• B. 2.26 eV
• C. 1.81 eV
• D. 3.4 eV

Answer 1

The correct option is C 1.81 eV

Using the Einstein's equation for photoelectric , $\frac{1}{2}m{v}_1^2=\frac{hc}{{\lambda }_1}-W$ $....\left(1\right)$ and

$\frac{1}{2}m{v}_2^2=\frac{hc}{{\lambda }_2}-W$ $....\left(2\right)$

$\left(1\right)/\left(2\right)\Rightarrow \frac{v_1^2}{v_2^2}=\frac{hc/{\lambda }_1-W}{hc/{\lambda }_2-W}$

or $\frac{9}{1}=\frac{hc/{\lambda }_1-W}{hc/{\lambda }_2-W}$

or $9hc/{\lambda }_2-9W=hc/{\lambda }_1-W$

or $W=\left(1/8\right)[9hc/{\lambda }_2-hc/{\lambda }_1]=\left(1/8\right)[9\times \frac{6.62\times {10}^{-34}\times 3\times {10}^8}{6000\times {10}^{-10}}-\frac{6.62\times {10}^{-34}\times 3\times {10}^8}{3000\times {10}^{-10}}]$

$=2.89\times {10}^{-19}J=1.81eV$ (as $1eV=1.6\times {10}^{-19}J$)