Physics - Modern Physics Question with Solution | TestHub

The work function $\Phi$ and threshold wavelength ${\lambda }_0$ are related by the equation:

$\Phi =\frac{hc}{{\lambda }_0}$

This implies that the threshold wavelength is inversely proportional to the work function:

${\lambda }_0\propto \frac{1}{\Phi }$

The ratio of the threshold wavelength of sodium to that of copper is:

$\frac{{\lambda }_{0,Na}}{{\lambda }_{0,Cu}}=\frac{{\Phi }_{Cu}}{{\Phi }_{Na}}$

Substituting the given values:

$\frac{{\lambda }_{0,Na}}{{\lambda }_{0,Cu}}=\frac{4.5}{2.3}\approx 1.96$

This value is nearest to $2$, so the ratio is approximately $2:1$.

Answer: $2:1$