Stopping power of ionizing radiation

In summary: MeV/cmIn summary, The Bethe formula (-dE/dx) can be calculated for both alpha and beta particles. For beta particles, the minimum dE/dx for unit charge particles in air is about 1.81 MeV per gram/cm2. For alpha particles, the dE/dx is likely to be 200 to 400 MeV per gram/cm2. The value of K/A in the dE/dx equation is 0.307 MeV per gram/cm2. For low energy alphas in air, at βγ = 3, the dE/dx is
  • #1
CloudChamber
29
1
Hello All,
can anyone fill in the Bethe formula (-dE/dx) with
a. the information for an alpha particle?
b. the information for a beta particle?
Either one would be great!
 
Science news on Phys.org
  • #2
A good discussion of the dE/dx formula for beta particles in beta decay is given in Eq 27.3 of http://pdg.lbl.gov/2010/reviews/rpp2010-rev-passage-particles-matter.pdf. You don't mention what material you would like dE/dx for, but I suspect it is for air. A typical beta decay energy is ~ 0.5 to 1 MeV, so βγ ≈1. In Fig. 27.1, the dE/dx min at this energy is ≈1.5 MeV per gram/cm2 (in copper). In the following table, http://pdg.lbl.gov/2010/reviews/rpp2010-rev-atomic-nuclear-prop.pdf the minimum dE/dx for unit charge particles in air is about 1.81 MeV per gram/cm2.

For alpha particles from alpha decay, βγ << 1. so using the same plot, but multiplying by z2 = 22 = 4 for alphas, dE/dx is probably 200 to 400 MeV per gram/cm2.

For numbers, use the value of K/A in the dE/dx equation in Table 27.1: K/A = 0.307 MeV per gram/cm2

Note: (βγ)2 = γ2 - 1
 
Last edited:
  • #3
Here in attachment is calculation of dE/dx for low energy alphas in air. Note that at β γ = 3, dE/dx = 7.25 MeV per gram/cm2, which is 4 times the expected 1.81 MeV per gram/cm2 for singly charged particles. To get MeV per cm of air, multiply by 0.00122 grams per cm3.
 

Attachments

  • Alphaprog1.jpg
    Alphaprog1.jpg
    42.1 KB · Views: 513
  • AlphadEdx1.jpg
    AlphadEdx1.jpg
    34.1 KB · Views: 576
  • #4
Here is the same dE/dx program with only the charge and the mass changed to calculate the electron stopping power. Of course, electron straggling is very large, and is not included. Note that the minimum ionization of 1.81 MeV per gram/cm2 is at βγ = 3. A good rough dE/dx value for all beta decay betas is ≈2 MeV per gram/cm2,
 

Attachments

  • dEdx­_beta_air1.jpg
    dEdx­_beta_air1.jpg
    32.2 KB · Views: 460
  • #5


Hello, the Bethe formula for stopping power (-dE/dx) takes into account the energy loss per unit distance traveled by a charged particle in a material. The formula is given by:

-dE/dx = Kz^2Z/A * (1/β^2) * ln[(2meβ^2c^2)/(I(1-β^2))]

Where:
K = 0.307 MeV cm^2/g
z = charge of the particle (2 for alpha, -1 for beta)
Z = atomic number of the material
A = atomic mass of the material
β = velocity of the particle (v/c)
me = electron mass
c = speed of light
I = mean excitation energy of the material

For an alpha particle, we can plug in the following values:
z = 2
Z = atomic number of the material
A = atomic mass of the material
β = 0.1 (a typical velocity for an alpha particle)
I = mean excitation energy of the material (can be found in tables)

For a beta particle, we can use the following values:
z = -1
Z = atomic number of the material
A = atomic mass of the material
β = 0.9 (a typical velocity for a beta particle)
I = mean excitation energy of the material (can be found in tables)

I hope this helps! Please note that the values for Z, A, and I will vary depending on the material the particle is traveling through.
 

1. What is "Stopping power of ionizing radiation"?

The stopping power of ionizing radiation refers to the ability of a material to reduce the energy of ionizing radiation as it passes through it. It is a measure of how well a material can shield or protect against ionizing radiation.

2. How is stopping power calculated?

Stopping power is calculated by measuring the energy of the ionizing radiation before and after it passes through a material. The difference in energy is then used to determine the amount of energy that was absorbed by the material, which is the measure of its stopping power.

3. What factors affect the stopping power of a material?

The stopping power of a material is affected by its density, atomic composition, and thickness. Materials with higher densities or higher atomic numbers tend to have higher stopping powers, while thicker materials offer more protection against ionizing radiation.

4. How is the stopping power of different types of ionizing radiation compared?

The stopping power of different types of ionizing radiation can be compared using a quantity called linear energy transfer (LET). This measures the amount of energy deposited by the radiation per unit distance traveled in a material. Materials with higher LET values have higher stopping powers for that type of radiation.

5. What are some common materials used for shielding against ionizing radiation?

Lead, concrete, and water are commonly used materials for shielding against ionizing radiation. Lead has a high density and atomic number, making it effective at stopping ionizing radiation. Concrete is also dense and can be easily molded into different shapes for shielding applications. Water is often used for shielding in medical settings due to its low cost and ability to absorb ionizing radiation.

Similar threads

Replies
49
Views
6K
Replies
9
Views
1K
  • Thermodynamics
Replies
7
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
6
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
4
Views
1K
Replies
3
Views
998
  • High Energy, Nuclear, Particle Physics
Replies
8
Views
1K
Replies
1
Views
8K
  • Introductory Physics Homework Help
Replies
7
Views
2K
Replies
2
Views
6K
Back
Top