NEET · Physics · STD 12 - 11. Dual nature of radiation and matter

If the mass of neutron is \(1.7 \times 10^{-27} \;kg\), then the de-Broglie wavelength of neutron of energy \(3\; eV\) is \(\left(h=6.6 \times 10^{34} \;J \cdot sec\right)\),

A \(1.6 \times 10^{-10}m\)
B \(1.65 \times 10^{-11}m\)
C \(1.4 \times 10^{-10}m\)
D \(1.4 \times 10^{-11}m\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(1.65 \times 10^{-11}m\)

Step-by-step Solution

Detailed explanation

\(\lambda=\frac{ h }{ P }=\frac{ h }{\sqrt{2 m _{ e } E }}\) \(\lambda=\frac{6.625 \times 10^{-34}}{\sqrt{2 \times 1.7 \times 10^{-27} \times 3 \times 1.6 \times 10^{-19}}}\)

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 the following aspects with the respective metal.

Aspects	Metal
\((a)\) The metal which reveals a maximum number of oxidation states	\((i)\) Scandium
\((b)\) The metal although placed in \(3 d\) block is considered not as a transition element	\((ii)\) Copper
\((c)\) The metal which does not exhibit variable oxidation states	\((iii)\) Manganese
\((d)\) The metal which in \(+1\) oxidation state in aqueous solution undergoes disproportionation	\((iv)\) Zinc

Select the correct option

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