Question

65. If \( a _{0} \) is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength ( \( \lambda \) ) of the electron present in the second orbit of hydrogen atom? [ n : any integer] (1) \( \frac{2 a_{0}}{n \pi} \) (2) \( \frac{8 \pi a_{0}}{n} \) (3) \( \frac{4 \pi a_{0}}{n} \) (4) \( \frac{4 n}{\pi a_{0}} \) Ans. (2)

Answer 1

Answer:(2) \(\frac{8 \pi a_{0}}{n}\)  

\(2 \pi r_{n}=n \lambda\)

\(2 \pi\left(4 \mathrm{a}_{0}\right)=\mathrm{n} \lambda \)

\(=\lambda=\frac{8 \pi \mathrm{a}_{0}}{\mathrm{n}}\)