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A doubly ionised lithium atom is hydroge...

A doubly ionised lithium atom is hydrogen like with atomic number Z = 3 . The wavelength of radiation required to excite the electron in `Li^(2+)` from first to third Bohr orbit will be ______ . (Ionisation energy of hydrogen atom is 13.6 eV)

A

72.53 Å

B

114.02 Å

C

212.52 Å

D

17.72 Å

Text Solution

Verified by Experts

The correct Answer is:
B
For hydrogen like atom,
`E_(n)=-(13.6)/(n^(2))xxZ^(2)`
Thus for `Li^(++)` atom (Z=3) we have
`E_(1)=(-13.6xx(3)^(2))/(3^(2))`
`=-13.6eV`
Thus the energy required to transfer an electron from `E_(1)` to `E_(3)` level is .
`E=E_(3)-E_(1)=-13.6-(-122.4)`
`= 108 .8eV`
`lambda=(hc)/(E)`
`((6.63xx10^(-34))xx(3xx10^(8)))/(108.8xx1.6xx10^(-19))`
`implies" "lambda=114.02 Å`
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