Question

If the energies of the two photons are in the ratio of $3 : 2$, their wavelengths will be in the ratio of

• A. $9 : 4$
• B. $2 : 3$
• C. $1 : 2$
• D. $3 : 2$

Answer 1

Answer: (B)

$2 : 3$

Answer 2

$E_{1}: E_{2}=\frac{hc}{\lambda_{1}}: \frac{h c}{\lambda_{2}}=\frac{1}{\lambda_{1}}: \frac{1}{\lambda_{2}}$
$3: 2=\frac{1}{\lambda_{1}}: \frac{1}{\lambda_{2}}=\frac{\lambda_{2}: \lambda_{1}}{\lambda_{1} \lambda_{2}}$
$\therefore \lambda_{2}: \lambda_{1}=3: 2$

or $\lambda_{1}: \lambda_{2}=2: 3$