જ્યારે ન્યૂટ્રોનના વેગથી ઈલેક્ટ્રોનનો વેગ \(x\) ગણો થાય ત્યારે એક ઈલેક્ટ્રોન અને એક ન્યુટ્રોનની તરંગલંબાઈ સમાન બનશે. તો \(x\) નું મૂલ્ય \(........\) છે. (નજીકનો પૂર્ણાંક) (ઈલેક્ટ્રોનનું દળ \(9.1 \times 10^{-31}\, kg\) અને ન્યુટ્રોનનું દળ \(1.6 \times 10^{-27} \,kg\) )

A \(1757\)
B \(1758\)
C \(1756\)
D \(1755\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(1758\)

Step-by-step Solution

Detailed explanation

\(v_{e}=x v_{N}\) \(\lambda_{ e }=\lambda_{ N }\) \(\Rightarrow \frac{ h }{ m _{ e } v _{ c }}=\frac{ h }{ m _{ N } v_{ N }}\) \(v_{ e }=\frac{ m _{ N }}{ m _{ e }} \cdot v _{ N }\) \(=\frac{1.6 \times 10^{-27}}{9.1 \times 10^{-31}} v_{ N }\) \(v_{ e }=1758.24 \times v_{ N }\)

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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