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Question
Find the radius of a hydrogen atom in the $n = 2$ state according to Bohr’s theory.
Question by OpenStax is licensed under CC BY 4.0.
Final Answer
$2.12 \times 10^{-10}\textrm{ m}$
Solution Video

OpenStax College Physics Solution, Chapter 30, Problem 13 (Problems & Exercises) (0:42)

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Video Transcript

This is College Physics Answers with Shaun Dychko. According to Bohr's theory, the radius of a hydrogen-like atom is the principal quantum number squared divided by the atomic number or the number of protons in the nucleus, in other words, multiplied by the Bohr radius. And <i>n</i> can be any number from 1 up to infinity. So in this case, we are told <i>n</i> is 2 so we have 2 squared over 1; 1 because it's a hydrogen atom in which case, the atomic number is 1, 1 proton times 0.529 times 10 to the minus 10 meters— Bohr radius— which is 2.12 times 10 to the minus 10 meters will be the radius of this atom.