Question

Lights of wavelengths $\lambda _{1}=340 \, nm$ and $\lambda _{2}=540 \, nm$ are incident on a metallic surface. If the ratio of the maximum speeds of the electrons ejected is $2$ , the work function of the metal is

• A. $2 \, eV$
• B. $1.85 \, eV$
• C. $1 \, eV$
• D. $1.5 \, eV$

Answer 1

Answer: (B)

$\lambda _{1}=350nm,\lambda _{2}=540nm,\frac{V_{1}}{V_{2}}=2\Rightarrow V_{1}=2V \, and \, V_{2}=V$
$\frac{ hc }{\lambda_{1}}=\phi+\frac{1}{2} m (2 V )^{2}$
$\frac{hc}{\lambda _{2}}=\phi+\frac{1}{2}mV^{2}$
$\frac{hc}{\lambda _{1}}-\frac{hc}{\lambda _{2}}\times 4=\phi-4\phi$
$hc\left(\right.\frac{4}{540 nm}-\frac{1}{340 nm}\left.\right)=3\phi$
$\phi=1.8eV$