Question

Match the LIST-I with LIST-II 

LIST-I	LIST-II
A. Mobility of electrons (\(\mu\))	I. \( Ne^2\tau/m \)
B. Drift velocity of electrons (\(v_d\))	II. \( \mu E \)
C. Electrical conductivity of conduction electrons (\(\sigma\))	III. \( \mu m/e \)
D. Relaxation time of electrons (\(\tau\))	IV. \( 1/\rho ne \)

Choose the correct answer from the options given below:

• A. A - I, B - II, C - IV, D - III
• B. A - I, B - III, C - II, D - IV
• C. A - IV, B - II, C - I, D - III
• D. A - III, B - IV, C - I, D - II

Hint:

Start with the most fundamental definitions you remember, like \(v_d = \mu E\) and \(\sigma = ne\mu\). Use these to derive the other relationships. Be prepared for potential typos (like N for n) in exam questions and use the process of elimination to find the best-fitting answer.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This question requires matching key parameters of electron transport in a conductor with their corresponding formulas. There appear to be typos in the provided options and lists, so we will derive the correct relationships and find the best match.
Step 2: Detailed Explanation of Correct Formulas:


B. Drift velocity of electrons (\(v_d\)): Drift velocity is the average velocity of charge carriers in a material due to an electric field (E). It is directly proportional to the electric field, with the constant of proportionality being the mobility (\(\mu\)). So, \( v_d = \mu E \). B matches II.
A. Mobility of electrons (\(\mu\)): Mobility is a measure of how quickly an electron can move through a metal or semiconductor. From the Drude model, it is defined as \( \mu = \frac{e\tau}{m} \), where \(\tau\) is the relaxation time. None of the options in LIST-II directly match this. However, let's examine the other terms.
C. Electrical conductivity (\(\sigma\)): Conductivity is the measure of a material's ability to conduct an electric current. It is given by \( \sigma = ne\mu \), where n is the electron density. Substituting the expression for \(\mu\), we get \( \sigma = \frac{ne^2\tau}{m} \). This perfectly matches option I (assuming 'N' in the option is a typo for 'n'). So, C matches I.
D. Relaxation time of electrons (\(\tau\)): This is the average time between collisions for an electron. We can rearrange the mobility formula: \( \tau = \frac{\mu m}{e} \). This perfectly matches option III. So, D matches III.

Now let's revisit A. Mobility (\(\mu\)). The formula in option IV is \(1/(\rho ne)\). Here \(\rho\) is resistivity. Since conductivity \(\sigma = 1/\rho\), this expression is \( \sigma / (ne) \). We know \( \sigma = ne\mu \), so \( \sigma/(ne) = \mu \). Thus, A matches IV.
Step 3: Final Answer Matching:
The correct pairings are:

A \(\rightarrow\) IV
B \(\rightarrow\) II
C \(\rightarrow\) I
D \(\rightarrow\) III
This sequence corresponds to option (C).