Question

The energy spacing between levels 1 and 2 is twice that between 2 and 3. If an electron makes a transition from level 3 to level 2, the radiation of wavelength λ is emitted. What possible radiation wavelengths might be produced by other transitions among the three energy levels?

Answer 1

Answer:$\lambda _3=\frac{\lambda }{3}$

Explanation:

Given

$E_3-E_2=\frac{hc}{\lambda }$

also $E_2-E_1=2\left ( E_3-E_2\right )$

Let wavelength produce during transition from 2 to 1 is $\lambda_0$

$\frac{hc}{\lambda _0}=2\frac{hc}{\lambda }$

$\lambda _0=\frac{\lambda }{2}$

For $E_3 to E_1 transition$

$E_3-E_1=E_3-E_2+E_2-E_1$

$E_3-E_1=\frac{hc}{\lambda }+2\frac{hc}{\lambda }$

$\frac{hc}{\lambda _3}=3\frac{hc}{\lambda }$

$\lambda _3=\frac{\lambda }{3}$