Question

A beam of $30\text{keV}$ electrons strikes different targets in different experiments. The cut-off wavelength of the continuous spectrum of X-rays generated by beam for any target is
(correct answer + 1, wrong answer - 0.25)

• A. $1.0\times {10}^{-6}\text{m}$
• B. $3.0\times {10}^{-\infty }\text{m}$
• C. $4.14\times {10}^{-11}\text{m}$
• D. dependent on the nature of the target

Answer 1

The correct option is C $4.14\times {10}^{-11}\text{m}$

The cut-off wavelength $\left({\lambda }_{\text{min}}\right)$ corresponds to an electron transferring (approximately) all of its energy to an X-Ray photon, thus producing a photon with the greatest possible frequency and least possible wavelength.
For $\lambda$
$\frac{hc}{{\lambda }_{\text{min}}}=KE$
${\lambda }_{\text{min}}=\frac{hc}{KE}$
${\lambda }_{\text{min}}=\frac{6.6\times {10}^{-34}\times 3\times {10}^8}{30\times {10}^3\times 1.6\times {10}^{-19}}=4.14\times {10}^{-11}\text{m}$