Question

What is the wavelength of the most energetic photon emitted in the Balmer series of the hydrogen atom?

• A. 645 nm
• B. 580 nm
• C. 280 nm
• D. 365 nm

Answer 1

Answer: (D)

For Balmer series
$\frac{1}{\lambda }=R\left[\frac{1}{2^2}-\frac{1}{n^2}\right]$ where $n=3,4,\mathrm{5.....}(i)$
By putting n = ∞ in equation (i), we obtain the series limit of the Balmer series
$\frac{1}{\lambda }=R\left[\frac{1}{2^2}-\frac{1}{{\infty }^2}\right]$
or $\lambda$ = 364.5 nm.
This is the shortest wavelength in the series
Energy of photon $E=\frac{hc}{\lambda }$
Since $E=\propto \frac{1}{\lambda }$
For shortest wavelength, energy of photon is the most.