Question

The transition, so that the de-Broglie wavelength of electrons becomes 3 times of its initial value in $H{e}^{+}$ ion will be:

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

Answer 1

The correct option is C $2\to 6$

The de-Broglie wavelength of electron is directly proportional to the principal quantum number n.
$\frac{{\lambda }_2}{{\lambda }_1}=\frac{n_2}{n_1}$
But $\frac{{\lambda }_2}{{\lambda }_1}=\frac{3}{1}$
Thus $\frac{n_2}{n_1}=\frac{3}{1}$
This is possible for the transition $2\to 6$.