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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 of the final state of the atom?

1. n = 4
2. n = 2
3. n = 16
4. n = 3

Correct answer: n = 4

Solution

The radius of a hydrogen atom in a given state is proportional to the square of the principal quantum number (n²). Given that the initial radius is 5.3 × 10⁻¹¹ m (n = 1) and the final radius is 21.2 × 10⁻¹¹ m, the ratio of radii is 21.2/5.3 = 4. Since n² = 4, n = 2. Thus, the final state corresponds to n = 4.

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