Modern Physics 1 Question 17

14. The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561\AA. The wavelength of the second spectral line in the Balmer series of singly ionized helium atom is

(2011)

(a) 1215\AA

(b) 1640\AA

(c) 2430\AA

(d) 4687\AA

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Solution:

n=1\longdiv First line of n=1 Second line of 

For hydrogen or hydrogen type atoms,

1λ=RZ21nf21ni2

In the transition from ninf

λ1Z21nf21ni2

λ2λ1=Z121nf21ni2Z221nf21ni2

λ2=λ1Z121nf21ni2Z221nf21ni2

Substituting the values, we have

=(6561\AA)(1)2122132(2)2122142=1215\AA



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