Question 224: Atoms & Nuclei

Question

The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 $$ 	imes $$ 10
-16
s. The frequency of revolution of the electron in its first excited state (in s
-1
) is :

Accepted Answer

Time period of revolution of electron in n
th
orbit
V = $${{2\pi r} \over V}$$
= $${{2\pi {a_0}\left( {{{{n^2}} \over Z}} ight)} \over {{V_0}\left( {{Z \over n}} ight)}}$$
$$ \Rightarrow $$ T $$ \propto $$ $${{{{n^3}} \over {{Z^2}}}}$$
$$ 	herefore $$ $${{{T_1}} \over {{T_2}}} = {{n_1^3} \over {n_2^3}}$$
$$ \Rightarrow $$ $${{1.6 	imes {{10}^{ - 16}}} \over {{T_2}}} = {1 \over {{{\left( 2 ight)}^3}}}$$
$$ \Rightarrow $$ T
2
= 1.6 $$ 	imes $$ 8 $$ 	imes $$ 10
-16
$$ 	herefore $$ f
2
= $${1 \over {{T_2}}}$$ = $${1 \over {1.6 	imes 8 	imes {{10}^{ - 16}}}}$$ = 7.8 $$ 	imes $$ 10
14

Answer

5.6 $$ 	imes $$ 10
12

Answer

1.6 $$ 	imes $$ 10
14

Answer

7.8 $$ 	imes $$ 10
14

Answer

6.2 $$ 	imes $$ 10
15

Atoms & Nuclei

The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 $ \times $ 10 -16 s. The frequency of revolution of the electron in its first excited state (in s -1 ) is :

Choose the correct answer: