Atomic Structure Question 400

Question: If the radius of first orbit of H atom is $ a_0 $ the de- Broglie wavelength of an electron in the third orbit is

Options:

A) $ 4\pi a_0 $

B) $ 8\pi a_0 $

C) $ 6\pi a_0 $

D) $ 2\pi a_0 $

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Answer:

Correct Answer: C

Solution:

  • $ r_{n}=a_0n^{2} $

$ r=a_0\times {{(3)}^{2}}=9a_0 $

$ mvr=\frac{nh}{2\pi }; $

$ mv=\frac{nh}{2\pi r}=\frac{3h}{2\pi \times 9a_0}=\frac{h}{6\pi a_0} $

$ \lambda =\frac{h}{mv}=\frac{h}{h}\times 6\pi a_0=6\pi a_0 $



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