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Question
In a hydrogen atom, the electron makes a transition from (n + 1)th level to the nth level. If n>>1, the frequency of radiation emitted is proportional to:
In a hydrogen atom, the electron makes a transition from (n + 1)th level to the nth level. If n>>1, the frequency of radiation emitted is proportional to:
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Solution
The correct option is C 1/n3
Solution:
- When an electron makes transition from higher level(n+1) to its lower level (n) the wavelength of emitted radiation is related as λ ∝ nx and frequency ν ∝ 1/λ
- Change in energy ΔE = hν = E final − E initial or ΔE∝ En+1 − En…………..(1)
- En ∝ −1/n2 and En+1 ∝ −1/(n+1)2
- As ΔE=hν ,we can say that ΔE ∝ ν …………(2)
- from equation (1) and (2)
- ν ∝ En+1 − En
- ν ∝ {[−1/(n+1)2]−[ −1/n2 ]}/n2(n+1)2
- ν ∝[(n+1)2−n2] /n2(n+1)2
- ν ∝ (1+2n)/n2(n+1)2
- as n>>1, ν ∝ 2n/n2n2
- ν ∝ 2/n3
- as 2 is constant, ν ∝ 1/n3
S0, the correct option is C.
1/n3
Solution:
- When an electron makes transition from higher level(n+1) to its lower level (n) the wavelength of emitted radiation is related as λ ∝ nx and frequency ν ∝ 1/λ
- Change in energy ΔE = hν = E final − E initial or ΔE∝ En+1 − En…………..(1)
- En ∝ −1/n2 and En+1 ∝ −1/(n+1)2
- As ΔE=hν ,we can say that ΔE ∝ ν …………(2)
- from equation (1) and (2)
- ν ∝ En+1 − En
- ν ∝ {[−1/(n+1)2]−[ −1/n2 ]}/n2(n+1)2
- ν ∝[(n+1)2−n2] /n2(n+1)2
- ν ∝ (1+2n)/n2(n+1)2
- as n>>1, ν ∝ 2n/n2n2
- ν ∝ 2/n3
- as 2 is constant, ν ∝ 1/n3
S0, the correct option is C.
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