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Question

Estimate the difference in energy between 1st and 2nd Bohr’s orbit for a hydrogen atom. At what minimum atomic number, a transfer from n=2 to n=1 energy level would result in the emission of X-rays with λ=3.0×108 m ? Which among the following hydrogen atom-like species does this atomic number correspond to:
(use value of RH=1.097×107 m1)

A
Z=3 i.e.Li2+ ion
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B
Z=2 i.e.He+ ion
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C
Z=4 i.e.Be3+ ion
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D
None of the above
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Solution

The correct option is B Z=2 i.e.He+ ion
For H-atom, the energy of a stationary orbit is determined as:
En=k2n2
Where, k=constant (2.18×1018)
ΔE (n=2 to n=1)=k[114] = 3k4
= 1.635×1018 J
For a H-like species, energy of a stationary orbit is determined as:
where, Z = atomic number
ΔE=kZ2[1n121n22]
= 1λ=ΔEhc=khc×Z2×[1114]
= RH×Z2×34
Z2=43λRH
Z2=43×1.097×107×3×108
Z2=4.05
Z=2 i.e. He+


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