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calculate the wave number , wavelength and frequency of the spectral line of hydrogen for the transition from `n_(2)=4" to "n_(1)=2.` (Given `R=1.097xx10^(7)m^(-1))`

Text Solution

Verified by Experts

(a) Wave number, `bar(v)=R((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
`=1.097xx10^(7)[1/2^(2)-1/4^(2)]=3/16xx1.097xx10^(7)=2.057xx10^(6)m^(-1)`
(b) Frequency, `bar(cv)=3xx10^(8)xx2.057xx10^(6)=6.17xx10^(14)Hz.`
Wavelength , `lamda=1/v=1/(2.057xx10^(6))=4.861xx10^(-7)m " or "4861Å`
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Knowledge Check

  • Find the recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 1 state (R=1.097xx10^(7) m^(-1)) :

    A
    `2.4 ms^(-1)`
    B
    `4.18 ms^(-1)`
    C
    `3.2 ms^(-1)`
    D
    `6.4 ms^(-1)`.

  • Find the recoil speed of a hydrogen atom after it emits a photon in going from n= 5 state to n= 1 state (R= 1.097 xx 10^7 m^(-1)):

    A
    `2.4 ms^(-1)`
    B
    `4.18 ms^(-1)`
    C
    `3.2 ms^(-1)`
    D
    `6.4 ms^(-1)`

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    Calculate the wavelength and wave numbers of the first and second lines in tbe Balmer series of hydrogen spectrum. Given R = 1.096xx10^(7) m^(-1)

    Calculate the wave number of the spectral line when electron jumps from the seond Bohr orbit to the ground state. R = 1.097xx 10^(7) m^(-1)

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    Calculate the shortest and longest wavelength of Balmer series of hydrogen atom. Given R=1.097 xx 10^(7)m^(-1) .

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