Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:
Which of the following transitions in\[H{{e}^{+}}\]ion will give rise to a spectral line which has the same wavelength as some spectral line in the hydrogen atom? (1) n = 4 to n = 2 (2) n = 8 to n = 4 (3) n = 6 to n = 3 (4) n = 6 to n = 2A) 1, 2 and 3 are correct
B) 1 and 2 are correct
C) 2 and 4 are correct
D) 1 and 3 are correct
Correct Answer: B
Solution :
Let the spectral line in the transition from \[n=p\]to\[n=q\]in hydrogen atom is same as the transition from\[n=a\]to\[n=b\]in helium atom. Then \[\left( \frac{1}{{{q}^{2}}}-\frac{1}{{{p}^{2}}} \right)=4\left( \frac{1}{{{b}^{2}}}-\frac{1}{{{a}^{2}}} \right)\] or \[\frac{1}{{{q}^{2}}}-\frac{1}{{{p}^{2}}}={{\left( \frac{2}{b} \right)}^{2}}-{{\left( \frac{2}{a} \right)}^{2}}\] This will be satisfied if\[b=2q\]and\[a=2p\]ie, a and b should be even integers and greater than 1.
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