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The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 1 state will be

Option 1 -

4.17 m/s          

Option 2 -

2.19 m/s

Option 3 -

4.34 m/s

Option 4 -

3.25 m/s

0 2 Views | Posted 2 months ago
Asked by Shiksha User

  • 1 Answer

  • P

    Answered by

    Payal Gupta | Contributor-Level 10

    2 months ago
    Correct Option - 1


    Detailed Solution:

    ΔE=13.6 (112−152)=13.6×2425eV

    ⇒hcλ=13.6×2425eV.......... (1)

    With the help of conservation of linear momentum, we can write

    hλ=mHvH⇒hcλ=cmHvH⇒vH=hcλcmH=13.6×2425×1.6×10−193×108×1.67×10−27=4.17m/s

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