Atomic Structure - Result Question 106

####82. Estimate the difference in energy between 1 st and 2 nd Bohr’s orbit for a hydrogen atom. At what minimum atomic number, a transition from n=2 to n=1 energy level would result in the emission of X-rays with l=3.0×108m ? Which hydrogen atom-like species does this atomic number correspond to?

(1993,5M)

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Solution:

  1. For H-atom, the energy of a stationary orbit is determined as

En=kn2 where, k= constant (2.18×1018J) ΔE(n=2 to n=1)=k(114)=34k =1.635×1018J

For a H-like species, energy of stationary orbit is determined as

En=kZ2n2

where, Z= atomic number

ΔE=kZ2(1n121n22) 1λ=ΔEhc=khcZ2(1114)=RHZ2×34 Z2=43RHλ=43×1.097×107×3×108=4.05 Z=2(He+)



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