Finding the distance of a gamma ray travels in lead

[jumbogala]

Homework Statement

The ‘half-thickness’ tells us the thickness of a given material needed to absorb half the incident photons from a particular source.

Find the average distance of a gamma ray in lead before its first collision.

I have a value for the half thickness (and equivalent half thickness) and the density of lead.

Homework Equations

The Attempt at a Solution

I'm not sure how to go from the half thickness to a distance. Since this is the distance needed to absorb half the photons, is this also the average distance the photons will travel?

 

[anathema]

If so, couldn't we just divide the half thickness by 2 to get the average distance?

your response to this forum post could be:

The half-thickness is indeed the distance at which half of the incident photons will be absorbed by the material. However, this does not necessarily mean that it is also the average distance the photons will travel before their first collision. This is because the photons may not travel in a straight path and may interact with other particles or fields along the way.

To find the average distance of a gamma ray in lead before its first collision, we can use the formula for mean free path, which is the average distance a particle travels before its first interaction. This can be calculated by taking the reciprocal of the product of the material's density and the cross section for the interaction of interest. In this case, the interaction of interest is the absorption of photons in lead.

Therefore, to find the average distance, we can use the formula:
Mean free path = 1/(density x cross section)

We can use the known value for the density of lead and the cross section for photon absorption in lead to calculate the average distance. This will give us a more accurate measure of the distance a gamma ray will travel before its first collision in lead, as compared to simply dividing the half-thickness by 2.

 

[kerimek]

If so, we can use the formula for linear attenuation coefficient, μ, which is equal to the natural log of 2 divided by the half thickness, t1/2. From there, we can use the formula for mean free path, λ, which is equal to 1/μρ, where ρ is the density of lead. This will give us the average distance a gamma ray will travel before its first collision in lead. However, it is important to note that this is an average and individual gamma rays may have different distances before their first collision depending on their energy and direction of travel. Additionally, the half thickness and density of lead may vary depending on the source of the gamma rays, so the calculated average distance may not be accurate for all scenarios. Further research and experimentation may be needed to determine a more precise value for the average distance a gamma ray travels in lead.