In Bohr's atomic model, how are orbital radius r and energy E related to orbit number n?

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NEET Chemistry QUESTION #7379

Question 1

In Bohr's atomic model, how are orbital radius \(r\) and energy \(E\) related to orbit number \(n\)?

\(r \propto n^2\) and \(E \propto \dfrac{1}{n^2}\)✔️
\(r \propto \dfrac{1}{n^2}\) and \(E \propto n^2\)
\(r \propto \dfrac{1}{n}\) and \(E \propto n\)
\(E \propto n^2\) and \(r \propto n^2\)

Correct Answer Explanation

Bohr's model relationships:
\(r_n = a_0 \cdot \dfrac{n^2}{Z}\) → \(r \propto n^2\)

\(E_n = -13.6 \cdot \dfrac{Z^2}{n^2}\) eV → \(E \propto -\dfrac{1}{n^2}\)

As orbit number increases, radius increases (electrons move farther out) while energy becomes less negative (electrons become less tightly bound). For hydrogen (Z=1): \(r_1 = 0.529\) Å (Bohr radius).

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