Question

Multiple-Concept Example 9 reviews the concepts that are important in this problem. An electron, traveling at a speed of 5.76 × 10⁷ m/s, strikes the target of an X-ray tube. Upon impact, the electron decelerates to one-quarter of its original speed, emitting an X-ray in the process. What is the wavelength of the X-ray photon?

Answer 1

E_i = 1/2mv²

E_f = 1/2m * (1/4v)² = 1/32mv²

change in energy = 15/32mv²

so,

15/32mv² = hc / $\lambda$

1.415e-15 = 6.63e-34 * 3e8 / $\lambda$

$\lambda$ = 1.405e-10 m