When a certain x ray is Compton scattered at right angles to its initial direction, the shift in its wavelength is λ _c = 2.4 pm 1 picometer = 10^-12 m). If the wavelength of this ray is 15.4 pm, the wavelength of the scattered x ray must be closest to A) 2.4 pm. B) 0.15 pm. C) 18 pm. D) 13 pm. E) 170 pm.

Question

Quizplus · Accepted Answer

According to Compton scattering, the change in wavelength of an X-ray photon is given by the formula:
Δλ = h/mc (1 - cosθ)
where
h = Planck's constant
m = mass of electron
c = speed of light
θ = angle of scattering

Given that the X-ray is scattered at right angles, cosθ = 0. Therefore, Δλ = h/mc.

Substituting the given values, we get:
Δλ = (1240 eV·nm/15.4 pm)·(2.4 pm/10^-12 m)/(511 keV/c^2/2.998 x 10^8 m/s)
Δλ ≈ 18 pm

Therefore, the wavelength of the scattered X-ray is closest to 18 pm, which is choice C.

When a Certain X Ray Is Compton Scattered at Right