The species and the levels n 1 , n 2 are: | TestHub

Passage / Comprehension

Paragraph for Q.8 to Q.9

A hydrogen-like species is present in a sample in which all atoms/ions are in excited levels A or B only, with principal quantum numbers $n_{1}$ and $n_{2}$ ( $E_{n_{2}} > E_{n_{1}}$ ), and none in any other level. On returning to the ground state the sample emits a total of 10 different lines, of which 3 lines are due to transitions between the levels $n_{1}$ and $n_{2}$ only. The energy difference $E_{n_{2}} - E_{n_{1}}$ is 8.70 eV. (Take the ground-state energy of hydrogen as -13.6 eV.)

The species and the levels $n_{1}$ , $n_{2}$ are:

Options:

Answer:

Solution:

10 lines in all means 5 levels: $\frac{n _{2} ( n _{2} - 1 )}{2} = 10$ , so $n_{2} = 5$ .

3 lines between $n_{1}$ and $n_{2}$ means 3 levels: $n_{2} - n_{1} = 2$ , so $n_{1} = 3$ .

$E_{5} - E_{3} = 13.6 Z^{2} (\frac{1}{9} - \frac{1}{25}) = 13.6 Z^{2} \times \frac{16}{225} = 0.967 Z^{2} eV = 8.70 eV$ .

$Z^{2} = 9$ , so $Z = 3$ , which is $Li^{2 +}$ .

Answer: (B).

Chemistry - Atomic Structure Question with Solution | TestHub

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