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The electron in a hydrogen atom jumps ba...

The electron in a hydrogen atom jumps back from an excited state to ground state, by emitting a photon of wavelength `lambda_(0) = (16)/(15R)`, where R is Rydbergs's constant. In place of emitting one photon, the electron could come back to ground state by

A

Emitting `3` photons of wavelength `lambda_(1), lambda_(2)` and `lambda_(3)` such that `(1)/(lambda_(1)) + (1)/(lambda_(2)) + (1)/(lambda_(3)) = 15R/16`

B

Emitting `2` photons of wavelength `lambda_(1), lambda_(2)` and `lambda_(3)` such that `(1)/(lambda_(1)) + (1)/(lambda_(2)) + (1)/(lambda_(3)) = 15R/16`

C

Emitting 2 photons of wavelength `lambda_(1)` and `lambda_(2)` such that `lambda_(1) + lambda_(2) = 16/15R`

D

Emitting `3` photons of wavelength `lambda_(1), lambda_(2)` and `lambda_(3)` such that `lambda_(1) + lambda_(2) + lambda_(3) = 16/15R`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`(1)/(lambda_(0)) = R[(1)/(1^(2)) - (1)/(n^(2))], n = 4`
(a) `(hc)/(lambda_(0)) = (hc)/(lambda_(1)) + (hc)/(lambda_(2)) rArr (1)/(lambda_(0)) = (1)/(lambda_(1)) + (1)/(lambda_(2))`
or ` (hc)/(lambda_(0)) = (hc)/(lambda_(1)) + (hc)/(lambda_(2)) + (hc)/(lambda_(3)) rArr (1)/(lambda_(0)) = (1)/(lambda_(1)) + (1)/(lambda_(2)) + (1)/(lambda_(3))`
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Knowledge Check

  • Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength lambda . If R is the Rydberg constant, then the principal quatum number n of the excited state is

    A
    `sqrt((lambdaR)/(lambdaR-1))`
    B
    `sqrt((lambda)/(lambdaR-1))`
    C
    `sqrt((lambdaR^2)/(lambdaR-1))`
    D
    `sqrt((lambdaR)/(lambda-1))`

  • A hydrogen atom ia in excited state of principal quantum number n . It emits a photon of wavelength lambda when it returnesto the ground state. The value of n is

    A
    `sqrt(lambda R (lambda R - 1))`
    B
    `sqrt((lambda (R - 1))/(lambda R))`
    C
    `sqrt((lambda R)/(lambda R - 1))`
    D
    `sqrt lambda (R - 1)`

  • An electron in a hydrogen atom makes a transition from first excited state to ground state . The equivelent currect due to circulating electron :

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