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Match each hydrogen-like species in List-I with the correct property from List-II. (r0 = 0.53 angstrom). List-I: (P) H atom, (Q) He+ ion, (R) Be3+ ion, (S) Li2+ ion. List-II: (1) Radius of 2nd orbit = 0.53 * 2 angstrom, (2) Energy of 4th orbit = -13.6 eV, (3) Radius of 3rd orbit = 0.53 * 3 angstrom, (4) Speed of electron in 1st orbit = 2.18 * 10⁸ cm/s, (5) Bohr's radius formula not applicable.

1. P -> 4; Q -> 1; R -> 2; S -> 3
2. P -> 1; Q -> 2; R -> 3; S -> 4
3. P -> 2; Q -> 1; R -> 3; S -> 4
4. P -> 1; Q -> 2; R -> 3; S -> 5

Correct answer: P -> 4; Q -> 1; R -> 2; S -> 3

Solution

H (Z=1): v1 = 2.18*10⁸ * 1/1 = 2.18*10⁸ cm/s. Matches (4). He+ (Z=2): r2 = (4/2)*0.53 = 2*0.53 = 0.53*2 ang. Matches (1). Be3+ (Z=4): E4 = -13.6 * 4²/4² = -13.6*16/16 = -13.6 eV. Matches (2). Li2+ (Z=3): r3 = (9/3)*0.53 = 3*0.53 = 0.53*3 ang. Matches (3). So P->4, Q->1, R->2, S->3.

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