λ=mvh $\begin{aligned}
& \mathrm{mvr}=\frac{\mathrm{nh}}{2 \pi} \
& \mathrm{mv}=\frac{\mathrm{nh}}{2 \pi \mathrm{r}} \
& \lambda=\frac{2 \pi \mathrm{rh}}{\mathrm{nh}} \
& \lambda \propto \frac{\mathrm{r}}{\mathrm{n}} \
& \frac{\lambda_1}{\lambda_4}=\frac{\mathrm{r}_1 \mathrm{n}_4}{\mathrm{n}_1 \mathrm{r}_4}=\frac{5.3 \times 10^{-11} \times 4}{1 \times 84.8 \times 10^{-11}} \
& \frac{\lambda_1}{\lambda_4}=\frac{1}{4}
\end{aligned}$
An electron in the ground state of the hydrogen atom has the orbital radius of 5.3 × 10^-11 ~m while that for the electron in third excited state is…
JEE Main 2025 — Physics Modern Physics
2025mcqeasy
An electron in the ground state of the hydrogen atom has the orbital radius of 5.3×10−11 m while that for the electron in third excited state is 8.48×10−10 m. The ratio of the de Broglie wavelengths of electron in the excited state to that in the ground state is
Official previous-year question
Held on 22 Jan 2025 · Verified 6 Jul 2026.
Options
- A
3
- B
16
- C
9
- D
4
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