When a beam of accelerated electrons hits a target,a continuous $X$-ray spectrum is emitted from the target. Which of the following wavelengths is absent in the $X$-ray spectrum,if the $X$-ray tube is operating at $40,000 \ V$?

  • A
    $0.25 \ \mathring{A}$
  • B
    $0.5 \ \mathring{A}$
  • C
    $1.5 \ \mathring{A}$
  • D
    $1 \ \mathring{A}$

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An $X$-ray tube operates at $50 \, kV$ and $20 \, mA$. The target material has a mass of $1.0 \, kg$ and a specific heat capacity of $495 \, J \cdot kg^{-1} \cdot ^\circ C^{-1}$. One percent of the applied electrical power is converted into $X$-rays,and the remaining energy is used to heat the target. Then:
$(1)$ $A$ suitable target material should have a high melting point.
$(2)$ $A$ suitable target material should have low thermal conductivity.
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$(4)$ The minimum wavelength of the emitted $X$-rays is $0.25 \, \mathring{A}$.

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The $K_{\alpha}$ $X$-ray emission from tungsten occurs at $\lambda = 0.021 \ nm$. The energy difference between the $K$ and $L$ levels in the atom is:

The dependence of the short wavelength limit $\lambda _{\min }$ on the accelerating potential $V$ is represented by the curve of figure.

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