Question

In hydrogen atom, which of the following transitions produce a spectral line of maximum frequency?

• A. $6\to 2$
• B. $2\to 1$
• C. $4\to 3$
• D. $5\to 2$

Answer 1

Answer: (B)

$2\to 1$

Frequency of photon emitted due to transitions $\nu =\frac{\Delta E}{h}$
where $\Delta E$ is the difference in energy of the states between which transition takes place.
Difference in energy between nth state and mth state is given by $\Delta E_{nm}=13.6(\frac{1}{n^2}-\frac{1}{m^2})eV$
Since, difference in energies of $2nd$ and $1st$ state is the maximum, so spectral line with maximum frequency is obtained when a transition takes place from $2\to 1$ .
$\Delta E_{12}=13.6(\frac{1}{1^2}-\frac{1}{2^2})eV=6.8eV$