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The electron in a hydrogen atom make a ...

The electron in a hydrogen atom make a transtion `n_(1) rarr n_(2)` where `n_(1) and n_(2)` are the priocipal quantum number of the two states . Assume the Bohr model to be valid . The time period of the electron in the initial state is eight time that in the final state . The possible values of `n_(1) and n_(2)` are

A

`n_(1)=4, n_(2)=2`

B

`n_(1)=8, n_(2)=2`

C

`n_(1)=8, n_(2)=1`

D

`n_(1)=6, n_(2)=3`

Text Solution

Verified by Experts

The correct Answer is:
A, D
According to Bohr model,
`r_(n) propto n^(2)" …(i)"`
`v_(n) propto 1/n" …(ii)"`
Now `T_(n)=(2pi)/omega=(2pir_(n))/(v_(n))" or "T_(n) propto r_(n)/v_(n)`
Using equation (i) and (ii), we get, `T_(n) propto n^(2)/(1//n)" or "T_(n) propto n^(3)`
`therefore (T_(n))_(1)/(T_(n))_(2)=n_(1)^(3)/n_(2)^(3)" or "8=(n_(1)/n_(2))^(3)`
or `n_(1)=2n_(2)" ...(iii)"`
Option (a) : `n_(1)=4, n_(2)=2`. It fulfills condition
Option (d) : `n_(1)=6, n_(2)=3`. It fulfills condition.
Options (a) and (d) are correct.
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