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Question

The ratio of the maximum to the minimum wavelengths of an electron that emits radiation is 1.8. What energy level (n) will its first excited state be at?

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Solution

We know,
λ1E

When an electron transits from to current level x.
1λmin=1RH(1x21) ...(i)

When an electron transits from (x+1) to current level x.
1λmax=1RH(1x21(x+1)2) ...(ii)

Dividing eqn (i) by eqn (ii), we get
λmaxλmin=1.8

1x2×1(1x21(x+1)2)=1.8

(x+1)22x+1=1.8

x21.6x0.8=0
(x2)(5x2)=0
x=2 (+ve value)
So 1st excited state will be: x+1=2+1=3


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