If a0 ​ is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength (λ) of the electron present ​

Question

If \(\mathrm{a}_{0}\) 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) \(\frac{4 \mathrm{n}}{\pi \mathrm{a}_{0}}\)

Answer 1

Correct option is (2) \(\frac{8 \pi a_{0}}{n}\)  

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

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

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