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Which of the following statement (s) is /are true?

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If H-atoms are in 3rd energy level, then number of maximum different spectral lines produced by 2 atoms will be equal to number of maximum spectral lines produced by 3 H-atoms.

For third excited state, He⁺ions and maximum number of different spectral line produced by 4 H-atoms are equal.

Energy evolved from 3rd to 2nd energy level transition in He⁺can be used to ionise Li ²⁺ from ground level.

Energy evolved by a He⁺ion which is in its 1st excited state can ionise a hydrogen atom which is in its ground state

answer is A, B, D.

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Detailed Solution

Here,

(a) 2 atoms : $[3 \to 2, 2 \to 1], [3 \to 1]$

3 atoms : $[3 \to 2, 2 \to 1], [3 \to 1], [3 \to 1]$ or $[3 \to 2, 2 \to 1]$

(b) 4 atoms: $[4 \to 3, 3 \to 2, 2 \to 1], [4 \to 2, 2 \to 1]$ $[4 \to 3, 3 \to 1], [4 \to 1]$

Maximum diff, lines = 6

For ${He}^{+} ion : \frac{4 (4 - 1)}{2} = 6$

(d) $ΔE = 10 .2 \times 2^{2} eV > 13 .6 eV$

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