Which one of the following has the largest energy content?

Question

Professor PC Thomas Classes · Answer

$$
\begin{gathered}
E=n \frac{h c}{\lambda} \
E \propto \frac{n}{\lambda}
\end{gathered}
$$Evaluating $\frac{n}{\lambda}$ for each option:
(a) $\frac{10^2}{10^{-12} \mathrm{~m}}=1.0 	imes 10^{14} \mathrm{~m}^{-1}$
(b) $\frac{10^5}{2 	imes 10^{-9} \mathrm{~m}}=0.5 	imes 10^{14} \mathrm{~m}^{-1}$
(c) $\frac{10^7}{300 	imes 10^{-9} \mathrm{~m}} \approx 0.33 	imes 10^{14} \mathrm{~m}^{-1}$
(d) $\frac{10^8}{600 	imes 10^{-9} \mathrm{~m}} \approx 1.67 	imes 10^{14} \mathrm{~m}^{-1}$
Option (d) yields the highest value.