TS EAMCET · Chemistry · Structure of Atom

Based on the Bohr's theory of hydrogen atom, the speed of the electron, energy of the electron and the radius of its orbit varies with the principal quantum number, respectively as

A \(n: n^2: n^2\)
B \(\frac{1}{n^2}: \frac{1}{n}: n\)
C \(\frac{1}{n}: \frac{1}{n}: n^2\)
D \(\frac{1}{n}: \frac{1}{n^2}: n^2\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{1}{n}: \frac{1}{n^2}: n^2\)

Step-by-step Solution

Detailed explanation

According to Bohr's theory of hydrogen at (i) The speed of electron in the \(n\)th orbit, \[ \begin{aligned} v_n & =\frac{1}{n} \frac{e^2}{4 \pi \varepsilon_0(h / 2 \pi)} \\ \text { or, } \quad v_n & \propto \frac{1}{n} \end{aligned} \] (ii) The energy of electron in the \(n\)th…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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