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A hydrogen atom initially in the ground level absorbs a photon and is excited to `n=4` level then the wavelength of photon is

Monjur Alahi

A hydrogen atom initially in the ground level absorbs a photon and is excited to `n=4` level then the wavelength of photon is
A. `790 Å`
B. `870 Å`
C. `970 Å`
D. `1070 Å`


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Salim Ahmed Kawsar

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Correct Answer - C
Here ,`n_1=1` and `n_2=4`
Energy of photon absorbed, `e=-e_2-e_1`
`E_n=-(13.6)/n^2eV`
Since,
`E_2-E_1=-(13.6)/(4)^2-(-(13.6)/((1)^2))`
`=-(13.6)/(16)+13.6=(13.6xx15)/(16)eV`
`=12.75eV=12.75xx1.6xx10^(-19)J=20.4xx10^(-19)J`
`E_2-E_1=(hc)/(lambda)`
`therefore lambda =(hc)/(E_2-E_1)=(6.6xx10^(-34)xx3xx10^(8))/(20.4xx10^(10^(-19)))`
`=9.70xx10^(-8)m=970xx10^(-10)=970Å`.

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