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The time period of revolution of electro...

The time period of revolution of electron in its ground state orbit in a hydrogen atom is `1.60xx 10 ^(-16)s.` The time period of revolution of the electron in its second excited state in a `He ^(+)` ion is:

A

`1.08xx10 ^(-15)s`

B

`1.30 xx10^(-15)s`

C

`2.30 xx10^(-14)s`

D

`2.08xx 10^(-14)s`

Text Solution

Verified by Experts

The correct Answer is:
A
Time -period `= T = (2pir )/(v)`
`T =(2pi a _(0))/(v _(1)). (n ^(2))/(Z) . (n)/(Z), " " T = (2 pi a _(0))/(v _(1)) . (n ^(3))/(Z ^(2))`
`T prop ( n ^(3))/( Z ^(2))" " therefore (T_(2))/(T_(1)) = (n _(2)^(3))/(n _(1)^(3))=27/1 .(1)/(4)`
`T_(2) = (27)/(1) T_(1) = (27)/(4) xx 1.6xx10^(-16) s = 1.08 xx10^(-15)s`
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