A photon having wavelength λ scatters off a free electron at A (see figure below), producing a second photon having wavelength λ'. This photon then scatters off another free electron at B, producing a third photon having wavelength λ'' and moving in a direction directly opposite the original photon as shown in the figure. Determine the value of Δλ = λ'' − λ.

What is Δλ in meter?

(If you google this question there is a diagram on the first link)

I know that this is the Compton effect
Δλ = λ- λo = (h/mc)(1-cos theta)
H/mc = 0.00243 nm

Then I'm not sure what to do

4.85pm

To calculate Δλ, you need to use the Compton scattering formula:

Δλ = λ - λ₀ = (h / mc) * (1 - cosθ)

From the information given, we know that the value of h/mc is 0.00243 nm. Now let's break down the steps to find the value of Δλ:

1. First, find the value of cosθ:
- Since the third photon is moving in a direction directly opposite the original photon, it means they have a 180° scattering angle.
- In this case, cosθ = cos(180°) = -1.

2. Substitute the values into the Compton scattering formula:
Δλ = (0.00243 nm) * (1 - (-1))

3. Simplify the equation:
Δλ = (0.00243 nm) * (1 + 1)
Δλ = (0.00243 nm) * 2
Δλ = 0.00486 nm

4. Convert Δλ from nanometers (nm) to meters (m):
1 nm = 1 x 10^(-9) m
Δλ = 0.00486 nm * (1 x 10^(-9) m/nm)
Δλ ≈ 4.86 x 10^(-12) m

So, Δλ is approximately 4.86 x 10^(-12) meters.

To determine the value of Δλ, you can use the formula given for the Compton effect:

Δλ = λ - λ₀ = (h/mc)(1 - cosθ)

where Δλ is the change in wavelength, λ is the initial wavelength of the photon, λ₀ is the final wavelength of the photon, h is Planck's constant, m is the rest mass of the electron, c is the speed of light, and θ is the scattering angle.

From the information provided, it seems that you have the value of h/mc, which is given as 0.00243 nm. To continue, you need to find the scattering angle θ, which is the angle between the incident and scattered photons.

Since the problem mentions a diagram, you can refer to it to obtain the scattering angle θ. The diagram should show the incident photon, the scattered photon at A, and the scattered photon at B. The angle θ can be measured as the angle between the incident and scattered photons at either A or B.

Once you have determined the value of θ, you can substitute it into the formula along with the initial wavelength λ to calculate Δλ.

Finally, to convert the value of Δλ to meters, you can use the conversion factor:

1 nm = 10^(-9) m

Multiply the calculated value of Δλ in nanometers by the conversion factor to obtain the value in meters.

0,071 nm