Sodium and copper have work functions 2.3 eV and 4.5 eV respectively. Then, the ratio of their threshold wavelengths is nearest to:
Answer & explanation
Correct answer: option 2
Work function, $W_0=hv_0$
For sodium, $W_{01}=hv_{01}=\frac{hc}{λ_0}$
$⇒\frac{2.3eV}{h}=v_{01}=\frac{c}{λ_{01}}$
For copper, $W_{02}=hv_{02}$
$⇒\frac{4.5eV}{h}=v_{02}=\frac{c}{λ_{02}}$
$⇒\frac{λ_{01}}{λ_{02}}=\frac{ch}{2.3}×\frac{4.5}{ch}=\frac{2}{1}$
$⇒λ_{01}:λ_{02}=2:1$