The curves P and Q schematically show the variation of X -ray intensity with
wavelength at two different accelerating voltages for a given target material. In the
figure 𝜆1 = 0.25 Å, 𝜆2 = 0.5 Å, 𝜆3 = 1.0 Å, and 𝜆4 = 2.25 Å. Take Planck's
constant as 6.6 × 10-34 Js, speed of light as 3 × 108 ms-1 and elementary charge
as 1.6 × 10-19 C.
Which of the following statement is/are true?
Options:
(A) The accelerating potential corresponding to curve P is greater than that of curve Q
(B) The accelerating potential applied to obtain curve Q is 24750 V
(C) Peaks (II) and (IV) correspond to radiative transitions from L to K shells
(D) Peaks (I) and (III) correspond to radiative transitions from N to K shells
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2024 Q.53)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Nuclear & Particle Physics:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
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