AIIMS 2017 Physics Conductivity and Mobility MCQ Question
A semiconductor has an electron concentration of 8×10¹³ per cm³ and a hole concentration of 5×10¹² per cm³. The electron mobility is 25000 cm²V⁻¹s⁻¹ and the hole mobility is 100 cm²V⁻¹s⁻¹. Then,
The semiconductor is n-type.
The conductivity is 320 m mho cm⁻¹
Both (a) and (b)
None of the above
Correct Answer
Detailed Explanation
To calculate the conductivity (σ) of the semiconductor, we use the formula σ = q(nμₑ + pμₕ), where q is the charge of an electron (approximately 1.6 × 10⁻¹⁹ C), n is the electron concentration (8 × 10¹³ cm⁻³), p is the hole concentration (5 × 10¹² cm⁻³), μₑ is the electron mobility (25,000 cm² V⁻¹ s⁻¹), and μₕ is the hole mobility (100 cm² V⁻¹ s⁻¹). Plugging in these values, we find that the conductivity is approximately 320 m mho cm⁻¹, confirming option B as correct.
Option A is incorrect because the electron concentration is greater than the hole concentration, indicating that the semiconductor is n-type; however, this does not negate the validity of option B. Option C is incorrect because while option B is true, option A is not, making both statements not simultaneously correct.
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