What was the angle of deflection?

In summary, the incident X-ray frequency was changed to 4.50 x 10^19 Hz and the deflected X-ray frequency was measured to be 4.32 x 10^19 Hz. Using the equations Δλ = λf - λi and Δλ = (h/mc)(1-cosθ), the wavelength of the X-ray before and after deflection was found to be 6.818181812 x 10^-12 m and 6.9444444444 x 10^-12 m, respectively. The change in wavelength was then used to find the angle of deflection, which was calculated to be 18.6°. This process can be verified by considering the physics behind the
  • #1
Ale_keys
1
0
Homework Statement
The scientist changes the frequency of the incident X-ray to 4.50 x 10^19 Hz and measures the deflected X ray frequency of 4.32 x 10^19 Hz. What was the angle of deflection?

Fi = 4.50 x 10^19 Hz
Ff = 4.32 x 10^19 Hz

2. Homework Equations
Δλ = λf - λi
Δλ = (h/mc)(1-cosθ)
λ = c/f

3. The Attempt at a Solution

First, I found the wavelength of the X ray before and after it is deflected.

λi = c/f
= (3.00 x 10^8 m/s) / (4.50 x 10^19 Hz)
= 6.818181812 x 10^-12 m

λf = c/f
= (3.00 x 10^8 m/s) / (4.32 x 10^19 Hz)
= 6.9444444444 x 10^-12 m

Then found the change in wavelength

Δλ = λf - λi
= (6.944444444 x 10^-12 m) - (6.818181812 x 10^-12 m)
= 1.26262626 x 10^-13 m

Then I used the change in wavelength to find the angle

Δλ = (h/mc)(1-cosθ)
1.26262626 x 10^-13 m = ((6.63 x 10^-34 Js) / (9.11 x 10^-31 kg)(3.00 x 10^8 m/s))(1-cosθ)
1.26262626 x 10^-13 m = (2.4259056 x 10^-12)(1-cosθ)
0.052047623 = 1-cosθ
cosθ = 0.947952377
cos^-1(0.947952377) = 18.56692499° = 18.6°

I'm just really unsure of the process that I took...
 
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  • #2
Welcome to PF;
Please do not leave out vital information - I am guessing that this is a Compton effect problem.

The way to be more sure of the processes you used, is to write down your reasoning for each step: why did you choose that particular equation?
You should also consider if the answer makes sense in terms of the physics - i.e. if you already know the deflection angle for another frequency, you can compare the deflection angles ... how does the deflection angle generally depend on the frequency: i.e. does a higher frequency produce a bigger or a smaller angle?
 

Related to What was the angle of deflection?

1. What is the angle of deflection?

The angle of deflection refers to the deviation of a moving object from its original path as a result of encountering an obstacle or force.

2. How is the angle of deflection measured?

The angle of deflection is typically measured in degrees using a protractor or other measuring tool to determine the angle between the original path and the deflected path.

3. What factors affect the angle of deflection?

The angle of deflection can be affected by several factors, including the velocity and direction of the moving object, the magnitude and direction of the force acting on the object, and the properties of the obstacle or surface the object encounters.

4. Can the angle of deflection be predicted?

In some cases, the angle of deflection can be predicted using mathematical equations and principles such as Newton's laws of motion. However, it may be more difficult to predict in real-world situations where there are multiple variables and factors at play.

5. How is the angle of deflection used in science and engineering?

The concept of angle of deflection is used in various fields of science and engineering, such as physics, mechanics, and aerodynamics. It helps to understand and predict the behavior of moving objects and design structures and mechanisms for optimal performance and safety.

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