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JEE MainPhysicsAtomic Physics

The radius of the n^ th orbit of Li ²⁺ is r₁ and the radius of the 2^ nd orbit of He ⁺ is r₂ . If the ratio r₁ r₂ is 6 , the value of n is _____.

Correct answer

6

Step-by-step solution

The radius of the n^ th Bohr orbit is given by r = r₀ n^2 Z , where r₀ is the Bohr radius. For the n^ th orbit of Li ²⁺ ( Z=3 ): r₁ = r₀ n^2 3 For the 2^ nd orbit of He ⁺ ( Z=2 ): r₂ = r₀ 2^2 2 = 2r₀ Given that the ratio r₁ r₂ = 6 : r₀ n^2 3 2r₀ = 6 n^2 6 = 6 n^2 = 36 n = 6 . Answer: 6

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