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Question

A sample of hydrogen atoms in the ground state is excited by a monochromatic radiation of wavelength λo A. The resulting spectrum consists of a maximum of 15 different lines. What is the wavelength λ?
(RH=109737 cm1)

A
937.3o A
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B
1025o A
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C
1236o A
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D
None of these
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Solution

The correct option is A 937.3o A
For a transition from n2 to n1, the maximum possible lines is given by (n2n1)(n2n1+1)2
For the given H-atom (n1=1), 15 lines are observed.
15=(n21)n22
n2=6
Thus, the electron is excited upto the 6th energy level.
So,
1λ=RH[112162]

=109677×3536 cm1

λ=9.373×106 cm1=937.3o A

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