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Question
The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10−11 m. What are the radii of the n = 2 and n = 3 orbits?
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Solution
The radius of the innermost orbit of a hydrogen atom, r1 = 5.3 × 10−11 m
Let r2 be the radius of the orbit at n = 2. It is related to the radius of the innermost orbit as:
r2 = (n)2r1
= (2)2 × 5.3 × 10−11
= 4 × 5.3 × 10−11
= 2.12 × 10−10 m
For n = 3, we can write the corresponding electron radius as:
r3 = (n)2r1
= (3)2 × 5.3 × 10−11
= 9 × 5.3 × 10−11
= 4.77 × 10−10 m
Hence, the radii of an electron for n = 2 and n = 3 orbits are 2.12 × 10−10 m and 4.77 × 10−10 m, respectively.
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