Question

X-rays of wavelength λ = 0.140 nm are scattered from carbon.

Part A

What is the Compton wavelength shift for photons detected at angle (relative to the incident beam) of exactly 45.0 ∘?

Express your answer to three significant figures and include the appropriate units.

Part B

What is the Compton wavelength shift for photons detected at angle (relative to the incident beam) of exactly 60.0 ∘?

Express your answer to three significant figures and include the appropriate units.

Part C

What is the Compton wavelength shift for photons detected at angle (relative to the incident beam) of exactly 150 ∘?

Express your answer to three significant figures and include the appropriate units.

Answer 1

A

Compton shift = (h/mc)*[1-cos theta)

Compton Shift = (6.6810^-34/9.1*10^-31*3*10^8) [1-cos 45]

Compton shift = 0.244*10^-11 * 0.292

Compton Shift = 0.07*10^-11 m

B)

Compton shift = (h/mc)*[1-cos theta)

Compton Shift = (6.6810^-34/9.1*10^-31*3*10^8) [1-cos 60]

Compton shift = 0.24*10^-11 * 0.5

Compton Shift = 0.12*10^-11 m

C)

Compton shift = (h/mc)*[1-cos theta)

Compton Shift = (6.6810^-34/9.1*10^-31*3*10^8) [1-cos 150]

Compton shift = 0.244*10^-11 * 1.866

Compton Shift = 455*10^-14 m

Answer 2

SOLUTION : 

Line passes through points (-4, -3) and (1, 2) 

So, slope of the required line  = - (2 - (-3))/(1 - (-4)) = 5/5 = 1

Equation of the required line in point slope form will be :

(y - 2) = 1 ( x - 1)

=> (y - 2) = 1 (x - 1). ANSWER.

Converting it into slope intercept form :

=> y = x - 1 + 2 

=> y = x + 1 

So, equation of the required line in slope-intercept form :

y = x + 1   (ANSWER).

SOLUTION :

Part A :

Compton shift at an angle 45º :

= Change in wavelength 

= Compton wave length * ( 1 - cos theta) 

= 0.00243 * 10^(-9) * ( 1 - cos(45))

= 7.1173 * 10^(-13) m (ANSWER).

Part B : 

Compton shift at an angle 60º :

= Change in wavelength 

= Compton wave length * ( 1 - cos theta) 

= 0.00243 * 10^(-9) * ( 1 - cos(60))

= 1.215 * 10^(-12) m (ANSWER).

Part C : 

Compton shift at an angle 150º :

= Change in wavelength 

= Compton wave length * ( 1 - cos theta) 

= 0.00243 * 10^(-9) * ( 1 - cos(150))

= 4.534 * 10^(-12) m (ANSWER)