Atoms And Nuclei Question 71

Question: The radius of hydrogen atom in its ground state is $ 5.3\times {{10}^{-11}}m $ . After collision with an electron it is found to have a radius of $ 21.2\times {{10}^{-11}}m $ . What is the principal quantum number n of the final state of the atom [CBSE PMT 1994; CPMT 2001; MH CET 2000]

Options:

A) n = 4

B) n = 2

C) n = 16

D) n = 3

Show Answer

Answer:

Correct Answer: B

Solution:

$ r\propto n^{2}\ i.e.\frac{r_{f}}{r_{i}}={{( \frac{n_{f}}{n_{i}} )}^{2}} $
Þ $ \frac{21.2\times {{10}^{-11}}}{5.3\times {{10}^{-11}}}={{( \frac{n}{1} )}^{2}} $
Þ $ n^{2}=4 $
Þ n = 2



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