Question

The figure shows the energy level of certain atom. When the electron deexcites from $3E$ to E, an electromagnetic wave of wavelength $\lambda$ is emitted. What is the wavelength of the electromagnetic wave emitted when the electron deexcites from $\frac{5E}{3}$ to E?

• A. $3\lambda$
• B. $2\lambda$
• C. $5\lambda$
• D. $\frac{3\lambda }{5}$

Answer 1

The correct option is A $3\lambda$

Wavelength of photon emitted $\lambda =\frac{hc}{\Delta E}$

Electron deexcites from 3E to E :

Wavelength emitted $\lambda =\frac{hc}{3E-E}=\frac{hc}{2E}$

Electron deexcites from 5E/3 to E :

Wavelength emitted ${\lambda }^{\prime }=\frac{hc}{\frac{5E}{3}-E}=\frac{3hc}{2E}$

$⟹$ ${\lambda }^{\prime }=3\lambda$