When a certain X ray is Compton scattered at right angles to its initial direction,the shift in its wavelength is $\lambda$_c = 2.4 pm (1 picometer = 10^-12 m).If the wavelength of this X 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 formula, 
Δλ = (h/mc)(1-cosθ)λ 
Where Δλ = shift in wavelength
θ = angle between incident and scattered beam
h = Planck's constant
m = mass of electron
c = speed of light
λ = initial wavelength

Here, Δλ = 2.4 pm (given)
θ = 90° (at right angles)
λ = 15.4 pm (given)

Substituting the values in the above formula, we get
2.4 pm = (h/mc)(1-cos90°)×15.4 pm
2.4 pm = (h/mc)×15.4 pm
(multiplying both sides by mc/15.4)

⇒ (h/mc) = 2.4/15.4

Now, the wavelength of scattered X-ray can be calculated using
λ' = λ + Δλ

Substituting the values, we get
λ' = 15.4 pm + 2.4 pm
λ' = 17.8 pm

Therefore, closest to 17.8 pm is option C) 18 pm.

When a Certain X Ray Is Compton Scattered at Right λ\lambdaλ

When a Certain X Ray Is Compton Scattered at Right $\lambda$