Verified Solution • 2025–26 Session moderate

QJEEM25Phd784: JEE Main 2025 Physics - Class 12 JEEM25Phd784 Solution: An electron in the ground state of the hydrogen atom has the…

An electron in the ground state of the hydrogen atom has the orbital radius of $5.3 \times 10^{-11} \mathrm{~m}$ while that for the electron in third excited state is $8.48 \times 10^{-10} \mathrm{~m}$ . The ratio of the de Broglie wavelengths of electron in the ground state to that in the excited state is

Multiple Choice Options

A 4
B 3
C 9
D 16

Step-by-Step Verified Solution

$\begin{aligned} λ = \frac{h}{mv} \\ mvr = \frac{nh}{2 π} \\ mv = \frac{nh}{2 π r} \\ λ = \frac{2 π rh}{nh} \\ λ \propto \frac{r}{n} \\ \frac{λ_{1}}{λ_{4}} = \frac{r_{1} n_{4}}{n_{1} r_{4}} = \frac{5.3 \times 10^{- 11} \times 4}{1 \times 84.8 \times 10^{- 11}} \\ \frac{λ_{1}}{λ_{4}} = \frac{1}{4} \end{aligned}$

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