Question

If ${\lambda }_1$ and ${\lambda }_2$ denote the wavelengths of de Broglie waves for electrons in the first and second Bohr orbits in a hydrogen atom, then ${\lambda }_1/{\lambda }_2$ is equal to :

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

Answer 1

The correct option is B $\frac{1}{2}$

The De-Broglie wavelengths can be given by:

$\lambda =\frac{h}{mv}..\left(1\right)$

Since mass of electron remains same, we get

$\frac{{\lambda }_1}{{\lambda }_2}=\frac{v_2}{v_1}..\left(2\right)$

Now, by Bohr's postulates, we know that velocity of electron in $n^{th}$ orbit in inversely proportional to $n$.

Hence, Answer= $1/2$.