NEETPhysicsAtomic Physics
Match List-I with List-II regarding the radius of Bohr orbits for various hydrogen-like species, where a₀ is the Bohr radius of the hydrogen atom. List-I List-II (A) 2^ nd orbit of He ⁺ (I) 2a₀ (B) 3^ rd orbit of Li ²⁺ (II) 3a₀ (C) 1^ st orbit of He ⁺ (III) a₀/2 (D) 4^ th orbit of Be ³⁺ (IV) 4a₀ Choose the correct answer from the options given below:
Options
- A(A)-(III), (B)-(II), (C)-(I), (D)-(IV)
- B(A)-(I), (B)-(II), (C)-(III), (D)-(IV)
- C(A)-(II), (B)-(III), (C)-(IV), (D)-(I)
- D(A)-(I), (B)-(III), (C)-(II), (D)-(IV)
Correct answer
B. (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
Step-by-step solution
The radius of the n^ th Bohr orbit of a hydrogen-like species is given by r = a₀ n^2 Z , where a₀ is the Bohr radius. (A) For the 2^ nd orbit of He ⁺ ( n = 2, Z = 2 ): r = a₀ 2^2 2 = 2a₀ (B) For the 3^ rd orbit of Li ²⁺ ( n = 3, Z = 3 ): r = a₀ 3^2 3 = 3a₀ (C) For the 1^ st orbit of He ⁺ ( n = 1, Z = 2 ): r = a₀ 1^2 2 = a₀ 2 (D) For the 4^ th orbit of Be ³⁺ ( n = 4, Z = 4 ): r = a₀ 4^2 4 = 4a₀ Therefore, the correct matching is (A)-(I), (B)-(II), (C)-(III), (D)-(IV). Answer: (A)-(I), (B)-(II), (C)-(III), (D)-(IV)