AP EAMCET · PHYSICS · Current Electricity

In a metal, the charge carrier density is \(9.1 \times 10^{28} \mathrm{~m}^{-3}\) and its electrical conductivity is \(6.4 \times 10^7 \mathrm{~S} \mathrm{~m}^{-1}\). When an electric field of \(10 \mathrm{~N} \mathrm{C}^{-1}\) is applied to the metal, then the average time between two successive collisions of electrons in the metal is
\(\left(\right.\) Mass of electron \(=9.1 \times 10^{-31} \mathrm{~kg}\); charge of electron \(\left.=1.6 \times 10^{-19} \mathrm{C}\right)\)

A \(4.6 \times 10^{-14} \mathrm{~s}\)
B \(2.5 \times 10^{-13} \mathrm{~s}\)
C \(4.6 \times 10^{-13} \mathrm{~s}\)
D \(2.5 \times 10^{-14} \mathrm{~s}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(2.5 \times 10^{-14} \mathrm{~s}\)

Step-by-step Solution

Detailed explanation

\(\tau = \frac{\sigma m_e}{ne^2}\) \(\tau = \frac{(6.4 \times 10^7) \times (9.1 \times 10^{-31})}{(9.1 \times 10^{28}) \times (1.6 \times 10^{-19})^2}\) \(\tau = \frac{5.824 \times 10^{-23}}{2.3296 \times 10^{-9}}\) \(\tau = 2.5 \times 10^{-14} \mathrm{~s}\)

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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