question_answer

Hydrogen \[{{(}_{1}}{{H}^{1}}),\]Deuterium\[{{(}_{1}}{{H}^{2}}),\] singly ionised Helium \[{{{{(}_{2}}H{{e}^{4}})}^{+}}\]and doubly ionised lithium \[{{{{(}_{3}}L{{i}^{6}})}^{++}}\]all have one electron around the nucleus. Consider an electron transition from n = 2 to n = l. If the wave lengths of emitted radiation are \[{{\lambda }_{1}},{{\lambda }_{2}},{{\lambda }_{3}}\]and \[{{\lambda }_{4}}\]respectively then approximately which one of the following is correct?         [JEE MAIN 2014]

A) \[{{\lambda }_{1}}={{\lambda }_{2}}=4{{\lambda }_{3}}=9{{\lambda }_{4}}\]

B) \[{{\lambda }_{1}}=2{{\lambda }_{2}}=3{{\lambda }_{3}}=4{{\lambda }_{4}}\]

C) \[4{{\lambda }_{1}}=2{{\lambda }_{2}}=2{{\lambda }_{3}}={{\lambda }_{4}}\]

D) \[{{\lambda }_{1}}=2{{\lambda }_{2}}=2{{\lambda }_{3}}={{\lambda }_{4}}\]

Correct Answer: A

Solution :

[a]

[M = mass of mucleus]

[ mass of H − atom]

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