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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
X-rays

Concepts Of Physics MCQ Edition [Volume 2] · Physics · X-rays

Calculate the cutoff wavelength of the continuous X-rays produced...

Calculate the cutoff wavelength of the continuous X-rays produced by an X-ray tube operating at 30 kV30 \text{ kV}.

Options

  1. A82.8 pm82.8 \text{ pm}
  2. B41.4 pm41.4 \text{ pm}
  3. C41.4 nm41.4 \text{ nm}
  4. D20.7 pm20.7 \text{ pm}

Correct answer

B. 41.4 pm41.4 \text{ pm}

Step-by-step solution

The cutoff wavelength of continuous X-rays is given by the Duane-Hunt law:

\lambda_{\text\min} = \dfrac{hc}{eV}

Substituting the standard value hc≈1242 eV⋅nmhc \approx 1242 \text{ eV}\cdot\text{nm} and V=30 kV=30000 VV = 30 \text{ kV} = 30000 \text{ V}:

\lambda_{\text\min} = \dfrac{1242 \text{ eV}\cdot\text{nm}}{30000 \text{ eV}}

\lambda_{\text\min} = 0.0414 \text{ nm}

Since 1 nm=1000 pm1 \text{ nm} = 1000 \text{ pm}:

\lambda_{\text\min} = 41.4 \text{ pm}
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