Question

An electron is moving in an orbit of a hydrogen atom from which there can be a maximum of six transitions. An electron is moving in an orbit of another hydrogen atom from which there can be a maximum of three transitions. The ratio of the velocity of the electron in these two orbits is

• A. $\frac{1}{2}$
• B. $\frac{2}{1}$
• C. $\frac{5}{4}$
• D. $\frac{3}{4}$

Answer 1

The correct option is D $\frac{3}{4}$

Case-1, when a maximum of six transitions is possible, then we can figure out that 6 transitions are only possible when n=4. That's if the electron is in the fourth orbit, then only 6 transition as possible.

Similarly, for case2, the maximum number of 2 transitions are possible only when n=3 or the electron is in 3rd orbit.

And we know that velocity of any electron in an orbit is goven by

$V=\left(\frac{2\pi kZ{e}^2}{h}\right)\frac{1}{n}\to V\propto \frac{1}{n}$

which implies that for 1st and 2nd case.

$\frac{V_1}{V_2}=\frac{\left(\frac{1}{n_1}\right)}{\left(\frac{1}{n_2}\right)}=\frac{n_2}{n_2}=\frac{3}{4}$