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JEE Advanced levelOne or more correct optionsDifficulty 3 of 3as106

Which $He X^{+}$ transitions emit light of the same wavelength as some line of the hydrogen spectrum?

A $n = 8 \to n = 4$
B $n = 5 \to n = 3$
C $n = 4 \to n = 2$
D $n = 6 \to n = 4$

Answer: A, C, D

A He+ transition

2 n_{i} \to 2 n_{f}

has

4 R (1/ (4 n_{f}^{2}) - 1/ (4 n_{i}^{2}))

, equal to the hydrogen

n_{i} \to n_{f}

line. So

4 \to 2

matches H

2 \to 1

,

6 \to 4

matches H

3 \to 2

, and

8 \to 4

matches H

4 \to 2

. Levels 5 and 3 are odd, so

5 \to 3

has no hydrogen counterpart.

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