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Question

A double charged lithium atom is equivalent to hydrogen whose atomic number is 3. The wavelength of required radiation for emitting electron from first to third Bohr orbit in Li++ will be (Ionisation energy of hydrogen atom is 13.6 eV)

A
182.51 A
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B
177.17 A
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C
142.25 A
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D
113.74 A
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Solution

The correct option is D 113.74 A
Energy of a electron in nth orbit of a hydrogen like atom is given by
En=13.6Z2n2eV, and Z = 3 for Li
Required energy for said transition
ΔE=E3E1=13.6Z2(112132)=13.6×32[89]=108.8eV=108.8×1.6×1019J
Now using ΔE=hcΔEλ=6.6×1034×3×108108.8×1.6×1019=0.11374×107mλ=113.74A

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