Question

Which of the following electronic transitions in a hydrogen atom is accompanied with the emission of a radiation that has the least wavelength?

• A. $n=3\to n=2$
• B. $n=7\to n=3$
• C. $n=4\to n=1$
• D. $n=10\to n=4$

Answer 1

The correct option is C $n=4\to n=1$

The energy of radtiation after a transition is given by:
$E_n\propto R_H(\frac{1}{n_f^2}-\frac{1}{n_i^2})$
Wavelength is inversely proportional to energy:
$E=\frac{h}{c\times \lambda }$
So the energies would be proportional to:
a) $5/36R_h$, b) $40/441R_h$, c) $15/16R_h$,
d) $84/1600R_h$
Highest energy would have the least wavelength, that would be option (c).