The radius of hydrogen atom in its ground state is 5.3×10⁻¹¹ m. After collision with an electron it is found to have a radius of 21.2×10⁻¹¹ m. What is the principal quantum number n of the final state of the atom?

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(2) n=2. Given: rᵢ=5.3×10⁻¹¹ m at nᵢ=1, and r_f=21.2×10⁻¹¹ m. Idea: for hydrogen rₙ∝ n², so (r_f)/(rᵢ)=(n_f²)/(nᵢ²). (21.2×10⁻¹¹)/(5.3×10⁻¹¹)=4, so n_f²=4. n_f=2.

The radius of hydrogen atom in its ground state is 5.3×10⁻¹¹ m. After collision with an electron it is found to have a radius of 21.2×10⁻¹¹ m. What is the principal quantum number n of the final state of the atom?

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