JEE Mains · Physics · STD 12 - 12. atoms

Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of \(\mathrm{Li}^{++}\)ion in its ground state is given by \(\frac{1}{X} a_0\), where \(X=\) _______. (Where \(\mathrm{a}_0\) is the first Bohr's radius.)

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Answer & Solution

Correct Answer

(C) 3

Step-by-step Solution

Detailed explanation

\(\mathrm{r}=\mathrm{r}_0 \frac{\mathrm{n}^2}{\mathrm{z}} \& \mathrm{z}=3\) for \(\mathrm{Li}^{+2}\) and \(\mathrm{n}=1\) \(\therefore \mathrm{r}=\mathrm{r}_0 \frac{1^2}{3}=\frac{\mathrm{r}_0}{3} \quad \therefore \mathrm{x}=3\)

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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Match List-I with List-II.

List-I	List-II
A. \(\sin^2 \omega t\)	I. Periodic with time period \(T = \dfrac{\pi}{\omega}\) but not simple harmonic motion (SHM)
B. \(\sin^3(2\omega t)\)	II. Periodic with time period \(T = \dfrac{2\pi}{\omega}\) but Not SHM
C. \(\sin(\omega t) + \cos(\pi \omega t)\)	III. Periodic with time period \(T = \dfrac{\pi}{\omega}\) and SHM
D. \(\cos\omega t + \cos 2\omega t\)	IV. Non-periodic

Choose the correct answer from the options given below :

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