Question

The following diagram indicates the energy levels of $a$ certain atom when the system moves from $4E$ level to $E$ . A photo of wavelength ${\lambda }_1$ is emitted. The wavelength of photon produced during it's transition from $\frac{7}{3}E$ level to $E$ is ${\lambda }_2.$ The ratio $\frac{{\lambda }_1}{{\lambda }_2}$ will be

• A. $\frac{9}{4}$
• B. $\frac{4}{9}$
• C. $\frac{3}{2}$
• D. $\frac{7}{3}$

Answer 1

Answer: (B)

Transition from $4E$ to $E(4E-E)=\frac{hc}{{\left(\lambda \right)}_1}\Rightarrow {\left(\lambda \right)}_1=\frac{hc}{3E}\dots \dots \dots (i)$
Transition from $\frac{7}{3}E$ to $E\left(\frac{7}{3}E-E\right)=\frac{hc}{{\left(\lambda \right)}_2}\Rightarrow {\left(\lambda \right)}_2=\frac{3hc}{4E}\dots .(ii)$
From equation $(i)$ and $(ii)$ $\frac{{\lambda }_1}{{\lambda }_2}=\frac{4}{9}$