WBJEE · Physics · Atomic Physics
Let \(v_{n}\) and \(E_{n}\) be the respective speed and energy of an electron in the \(n\) th orbit of radius \(r_{n}\), in a hydrogen atom, as predicted by Bohr's model. Then.
- A plot of \(\frac{E_{n} r_{n}}{E_{1} r_{1}}\) as a function of \(n\) is a straight line of slope 0
- B plot of \(\frac{r_{n} v_{n}}{r_{1} v_{1}}\) as a function of \(n\) is a straight line of slope 1
- C plot of \(\ln \left(\frac{r_{n}}{r_{1}}\right)\) as a function of \(\ln (n)\) is a straight line of slope 2
- D plot of In \(\left(\frac{r E_{1}}{E_{n} r_{1}}\right)\) as a function of \(\ln (n)\) is a straight line of slope 4
Answer & Solution
Correct Answer
(D) plot of In \(\left(\frac{r E_{1}}{E_{n} r_{1}}\right)\) as a function of \(\ln (n)\) is a straight line of slope 4
Step-by-step Solution
Detailed explanation
We know that, \(v \propto \frac{1}{n}\) (speed) \(E_{n} \propto \frac{1}{n^{2}} \quad(\text { energy })\) \(r_{n} \propto n^{2}\) \(\therefore E_{n T_{n}} \propto n^{0}\) \(\therefore E_{n} r_{n} \propto E_{1} r_{1}\) \(\frac{E_{1} r_{1}}{E_{1} r_{1}}\)…
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