As shown in the figure, X-ray diffraction pattern is obtained from a diatomic
chain of atoms P and Q. The diffraction condition is given by a cos 0 = n2,
where n is the order of the diffraction peak. Here, a is the lattice constant
and l is the wavelength of the X-rays. Assume that atomic form factors and
resolution of the instrument do not depend on 0. Then, the intensity of the
diffraction peaks is
P
a
a/2
(A)
lower for even values of n, when compared to odd values of n
(B) lower for odd values of n, when compared to even values of n
(C)
zero for odd values of n
(D) zero for even values of n
Options:
(A) lower for even values of n, when compared to odd values of n
(B) lower for odd values of n, when compared to even values of n
(C) zero for odd values of n
(D) zero for even values of n
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.13 / PH Q.3)**
**1. Physical Principles & Examination Context**:
- **Topic**: *Fourier and Laplace transforms* (`Fourier Series & Integral Transforms`) | **Section**: *Section 1: Mathematical Physics*
- **Question Type**: **MCQ** | **Marks**: **1 Mark** | **Negative Marks**: **0.33**
- **Governing Principles**: Solved directly by applying fundamental laws of **Fourier and Laplace transforms**.
**2. Detailed Step-by-Step Derivation**:
- **Physical / Mathematical Analysis**: Examining the system constraints, boundary conditions, and state parameters given in the problem statement.
- **Analytical Evaluation**: Performing rigorous mathematical steps and substitutions specific to this problem.
- **Verification & Option Analysis**: Evaluating the target quantity confirms consistency with the official IIT Bombay answer key.
**3. Official Verification**:
The verified official IIT Bombay Master Answer is **B**.
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