JEE MAIN - Chemistry (2025 - 29th January Morning Shift - No. 9)
If $a$0 is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength (λ) of the electron present in the second orbit of hydrogen atom? [n : any integer]
$\frac{8 \pi a_0}{n}$
$\frac{2 a_0}{n \pi}$
$\frac{n a_0}{4 \pi}$
$\frac{4 \pi a_0}{n}$
Explanation
$$\begin{aligned}
& 2 \pi \mathrm{r}_{\mathrm{n}}=\mathrm{n} \lambda \\
& 2 \pi \cdot\left(4 \mathrm{a}_0\right)=\mathrm{n} \lambda \\
& =\lambda=\frac{8 \pi \mathrm{a}_0}{\mathrm{n}}
\end{aligned}$$
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