1. Tardigrade
  2. Question
  3. Physics
  4. A graph of √v (where v is the frequency of Kα line of the characteristic X-ray spectrum ) is plotted against the atomic number Z of the elements emitting the characteristic X-ray .The intercept of the graph on the z-axis is 1 and the slope of the graph is 0.5 × 108 in SI units. The frequency of the Kα line for an element of atomic number 41 is given as α × 1016 Hz. Find the value of α.

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Q. A graph of $\sqrt{v}$ (where $v$ is the frequency of $K_{\alpha}$ line of the characteristic $X$-ray spectrum ) is plotted against the atomic number $Z$ of the elements emitting the characteristic $X$-ray .The intercept of the graph on the $z$-axis is $1$ and the slope of the graph is $0.5 \times 10^{8}$ in $SI$ units. The frequency of the $K_{\alpha}$ line for an element of atomic number $41$ is given as $\alpha \times 10^{16} Hz$. Find the value of $\alpha$.

Atoms

Solution:

From the given information,
$\sqrt{v}=m[Z-1]$
$ \Rightarrow \sqrt{v}=5 \times 10^{7}(Z-1)$
For $Z=41, v=\left[5 \times 10^{7} \times(40)\right]^{2}$
$=400 \times 10^{16} Hz$