Hall effect for semiconductor type identification — assertion–reason Assertion (A): The Hall effect can determine whether a semiconductor sample is p-type or n-type. Reason (R): In a magnetic field, electrons and holes deflect in opposite transverse directions, producing a Hall voltage whose sign reveals the majority carrier type.

Introduction / Context:
The Hall effect is a fundamental transport phenomenon used to extract carrier sign, concentration, and mobility in semiconductors. Measuring the polarity of the Hall voltage is the simplest, most direct way to distinguish p-type from n-type material.

Given Data / Assumptions:

• Rectangular sample with current along x, magnetic field along z.
• Steady, uniform fields; negligible magnetoresistance for simplicity.
• Conventional definitions: positive Hall coefficient indicates hole dominance.

Concept / Approach:
Charge carriers moving in a magnetic field experience a Lorentz force q * (v × B), deflecting them transverse to both current and field. Because electrons and holes have opposite charge, they deflect to opposite sample edges, charging the sides differently. The resulting Hall electric field builds until magnetic and electric forces balance, establishing a measurable Hall voltage with a sign that identifies the majority carrier type.

Step-by-Step Solution:
Drive current I along x in a sample; apply magnetic field B along z.Carriers experience transverse force along ±y depending on charge sign.Accumulated charges create Hall voltage V_H across y; its polarity corresponds to p-type (positive R_H) or n-type (negative R_H).

Verification / Alternative check:
Hall coefficient R_H = E_y / (J_x * B_z) has opposite signs for holes and electrons. Experimental setups routinely use this to classify doping type before device processing.

Why Other Options Are Wrong:
Option (b) denies the explanatory link. Options (c) and (d) contradict well-established Hall physics. Option (e) rejects both truths.

Common Pitfalls:

• Confusing conventional current direction with electron motion; sign conventions must be applied carefully.
• Misinterpreting contact placement leading to an apparent sign error.

Final Answer:
Both A and R are true and R is correct explanation of A