Question

The energy of an $X$ -ray photon is $2\, keV$, then its Frequency will be:

• A. $ 3.2\times {{10}^{-6}} $ per sec
• B. $ 5\times {{10}^{17}}$ per sec
• C. $ 2\times {{10}^{17}}$ per sec
• D. $ 2\times {{10}^{18}}$ per sec

Answer 1

Answer: (B)

For the most favourable collision in which the electron loses, the whole of its energy in a single collision with the target atom, an X-ray photon of maximum energy $h v$ is emitted
$E=h v$
where $h$ is Planck's constant and $v$ is frequency.
Given, $E=2 \,keV $
$=2 \times 10^{3} \times 1.6 \times 10^{-19} \,J$
$\Rightarrow v =\frac{E}{h}=\frac{2 \times 10^{3} \times 1.6 \times 10^{-19}}{6.6 \times 10^{-34}} $
$=9.84 \times 10^{17}$
$ \approx 5 \times 10^{17} / s$
Note : Since, energy $\propto$ frequency, higher the energy higher the frequency.