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Question

# A hydrogen atom is in ground state. In order to get six lines in its emission spectrum, wavelengths of incident radiation should be,

A
800 ˚A
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B
825 ˚A
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C
975 ˚A
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D
1025 ˚A
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Solution

## The correct option is C 975 ˚AThe number of spectral lines emitted, during transition is, n(n−1)2 ⇒6=n2(n−1) ⇒12=n2−n ⇒n2−n−12=0 ⇒n2−4n+3n−12=0 ⇒n(n−4)+3(n−4)=0 ⇒(n+3)(n−4)=0 n=−3,4 Considering positive value, we have n=4 Now, 1λ=R(112−142) ⇒λ=1615R=975 ˚A Hence, (C) is the correct answer.

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