Structure of Atom

Question 1

The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes n = 2 → n = 3 and n = 4 → n = 6 transitions, respectively, is

Accepted Answer

1/4. For absorption, 1/λ = R_H(1/n₁² − 1/n₂²), so λ is inversely proportional to ΔE. For 2 → 3, ΔE = R_H(1/4 − 1/9) = 5R_H/36. For 4 → 6, ΔE = R_H(1/16 − 1/36) = 20R_H/576 = 5R_H/144. The ratio λ(2→3)/λ(4→6) equals the inverse ratio of the energies, (5R_H/144)/(5R_H/36) = 36/144 = 1/4.

Answer

1/36

Answer

1/16

Answer

1/9

Question 2

Energy and radius of the first Bohr orbit of He⁺ and Li²⁺ are [Given R_H = 2.18 × 10⁻¹⁸ J, a₀ = 52.9 pm]

Accepted Answer

Eₙ(Li²⁺) = −19.62 × 10⁻¹⁸ J; rₙ(Li²⁺) = 17.6 pm; Eₙ(He⁺) = −8.72 × 10⁻¹⁸ J; rₙ(He⁺) = 26.4 pm. For a one-electron species Eₙ = −R_H·Z²/n² and rₙ = a₀·n²/Z. With n = 1: for Li²⁺ (Z = 3), E = −2.18 × 10⁻¹⁸ × 9 = −19.62 × 10⁻¹⁸ J and r = 52.9/3 = 17.6 pm; for He⁺ (Z = 2), E = −2.18 × 10⁻¹⁸ × 4 = −8.72 × 10⁻¹⁸ J and r = 52.9/2 = 26.4 pm. The distractors keep the right numbers but shift the exponent to 10⁻¹⁶ or swap the two ions.

Answer

Eₙ(Li²⁺) = −8.72 × 10⁻¹⁸ J; rₙ(Li²⁺) = 26.4 pm; Eₙ(He⁺) = −19.62 × 10⁻¹⁸ J; rₙ(He⁺) = 17.6 pm

Answer

Eₙ(Li²⁺) = −19.62 × 10⁻¹⁶ J; rₙ(Li²⁺) = 17.6 pm; Eₙ(He⁺) = −8.72 × 10⁻¹⁶ J; rₙ(He⁺) = 26.4 pm

Answer

Eₙ(Li²⁺) = −8.72 × 10⁻¹⁶ J; rₙ(Li²⁺) = 17.6 pm; Eₙ(He⁺) = −19.62 × 10⁻¹⁶ J; rₙ(He⁺) = 17.6 pm

Question 3

Match List-I with List-II and choose the correct answer from the options given below. List-I (Quantum number): A. mₗ B. mₛ C. l D. n List-II (Information provided): I. Shape of orbital II. Size of orbital III. Orientation of orbital IV. Orientation of spin of electron

Accepted Answer

A-III, B-IV, C-I, D-II. The principal quantum number n fixes the size and energy of the orbital. The azimuthal quantum number l fixes its shape. The magnetic quantum number mₗ fixes its orientation in space. The spin quantum number mₛ gives the orientation of the electron’s spin. Hence A-III, B-IV, C-I, D-II.

Answer

A-III, B-IV, C-II, D-I

Answer

A-II, B-I, C-IV, D-III

Answer

A-I, B-III, C-II, D-IV

Q1.The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes n = 2 → n = 3 and n = 4 → n = 6 transitions, respectively, is

Q2.Energy and radius of the first Bohr orbit of He⁺ and Li²⁺ are [Given R_H = 2.18 × 10⁻¹⁸ J, a₀ = 52.9 pm]

Q3.Match List-I with List-II and choose the correct answer from the options given below.