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 $
Show Answer
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 $
