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JEE Advanced 2024Paper 2
Exam
JEE Advanced
Year
2024
Paper
Paper 2
Subject
Physics
Chapter
Electromagnetic Waves

JEE Advanced 2024 · Paper 2 · Physics · Electromagnetic Waves

A metal target with atomic number Z=46 is bombarded with a high...

A metal target with atomic number Z=46Z=46 is bombarded with a high energy electron beam. The emission of X-rays from the target is analyzed. The ratio rr of the wavelengths of the KαK_\alpha-line and the cut-off is found to be r=2r=2. If the same electron beam bombards another metal target with Z=41Z=41, the value of rr will be

Options

  1. A2.53
  2. B1.27
  3. C2.24
  4. D1.58

Correct answer

A. 2.53

Step-by-step solution

1λα=34R(Z−1)2pλcut =hceV⇒ Ratio ∝1(Z−1)2 for same beam Zx=402452⇒x=452402.2≈2.53\begin{aligned} & \frac{1}{\lambda_\alpha}=\frac{3}{4} R(Z-1)^2 p \\ & \lambda_{\text{cut }}=\frac{h c}{e V} \\ & \Rightarrow \text{ Ratio } \propto \frac{1}{(Z-1)^2} \text{ for same beam } \\ & \frac{Z}{x}=\frac{40^2}{45^2} \\ & \Rightarrow x=\frac{45^2}{40^2} .2 \approx 2.53 \end{aligned})$
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