$\Delta \lambda$ is the difference between the wavelength of $k_\alpha$ line and the minimum wavelength of…

$\Delta \lambda$ is the difference between the wavelength of $k_\alpha$ line and the minimum wavelength of the continuous X-ray spectrum when the X-ray tube is operated at a voltage $V$. If the operating voltage is changed to $V / 3$, then the above difference is $\Delta \lambda^{\prime}$. Then
  1. $\Delta \lambda^{\prime}=5 \Delta \lambda$
  2. $\Delta \lambda^{\prime}=4 \Delta \lambda$
  3. $\Delta \lambda^{\prime}=3 \Delta \lambda$
  4. $\Delta \lambda^{\prime} < 3 \Delta \lambda$

Solution

$\begin{aligned} & \text { We know } \mathrm{eV}=\frac{h c}{\lambda} \Rightarrow \frac{V}{V^{\prime}}=\frac{\Delta \lambda^{\prime}}{\Delta \lambda} \\ & \Rightarrow \quad \frac{V}{V / 3}=\frac{\Delta \lambda^{\prime}}{\Delta \lambda} \\ & \Rightarrow \quad \Delta \lambda^{\prime}=3(\Delta \lambda)\end{aligned}$

Asked in: AP EAMCET 2004

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