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  • The wavelength of an electron revolving in the 3rd orbit of   is 'x'. The radius

The wavelength of an electron revolving in the 3rd orbit of Be^{3+}  is 'x'. The radius of the first Bohr orbit in the H atom is k, then 'x' is equal to?

Option: 1

6\pi k


Option: 2

5\pi k


Option: 3

\pi k


Option: 4

2\pi k


Answers (1)

best_answer

Answer:(a)  6\pi k

Explanation:

The wavelength of electron = x

The radius of first Bohr orbit i=k

 n=3

We get,

r_n=n^2r_1\\ r_{3}=\left(3\right)^2r_1\\ r_{3}=9r_1\\\ r_{1} = k ........\text{(given)}\\ r_{3}=9k_{1}\\
mvr=\frac{nh}{2\pi} \\ mv9k=\frac{3h}{2\pi}\\ \frac{h}{mv}=6\pi k\\ \frac{h}{mv}=\lambda\\ \lambda=x\\ x=6\pi k

Posted by

manish painkra

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