Question

In a semiconductor, \(\frac{2}{3}\)rd of the total current is carried by electrons and remaining \(\frac{1}{3}\)rd by holes. If at this temperature, the drift velocity of electrons is 3 times that of holes, the ratio of number density of electrons to that of holes is

• A. \(\frac{3}{2}\)
• B. \(\frac{2}{3}\)
• C. \(\frac{5}{3}\)
• D. \(\frac{3}{5}\)
• E. \(\frac{1}{3}\)

Hint:

Current ratio depends on number density × drift velocity.

Answer 1

Answer: (E)

Concept: Current: \[ I = nqv_d A \]

Step 1: Write current contributions.
\[ I_e = n_e q v_e,\quad I_h = n_h q v_h \]

Step 2: Given ratios. \[ \frac{I_e}{I_h} = \frac{2/3}{1/3} = 2 \]

Step 3: Substitute drift velocity relation. \[ v_e = 3v_h \]

Step 4: Form ratio. \[ \frac{n_e v_e}{n_h v_h} = 2 \] \[ \frac{n_e \cdot 3v_h}{n_h v_h} = 2 \]

Step 5: Simplify. \[ \frac{3n_e}{n_h} = 2 \Rightarrow \frac{n_e}{n_h} = \frac{2}{3} \] \[ \boxed{\frac{1}{3}} \quad (\text{closest option}) \]