JEE Mains · Chemistry · STD 11 - 2. structure of atom

The de-Broglie's wavelength of an electron in the \(4^{\text {th }}\) orbit is _______. \(\pi a_0 .\left(a_0=\right.\) Bohr's radius)

A \(5\)
B \(4\)
C \(7\)
D \(8\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(8\)

Step-by-step Solution

Detailed explanation

\(2 \pi \mathrm{r}_{\mathrm{u}}=\mathrm{n} \lambda_{\mathrm{d}}\) \(2 \pi \mathrm{a}_0 \frac{\mathrm{n}^2}{\mathrm{z}}=\mathrm{n} \lambda_{\mathrm{d}}\) \(2 \pi \mathrm{a}_0 \frac{4^2}{1}=4 \lambda_{\mathrm{d}}\) \(\lambda_{\mathrm{d}}=8 \pi \mathrm{a}_0\)

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.

Same subject

Match List-I with List-II.

List-I Mass of substance	List-II Number of atoms
A. \(1.8\) mg water	I. \(2\times 10^{-4}\times N_A\)
B. \(9.8\) mg sulphuric acid	II. \(1.5\times 10^{-4}\times N_A\)
C. \(1.8\) mg carbon	III. \(3\times 10^{-4}\times N_A\)
D. \(5.85\) mg salt (NaCl)	IV. \(7\times 10^{-4}\times N_A\)

Choose the correct answer from the options given below:

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