Range of electrons and beta particles 4.5.3



	You are here:		Chapter: 4 Atomic and nuclear physics Section: 4.5 Absorption of particles and dosimetry SubSection: 4.5.3 Range of electrons and beta particles

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4.5.3 Range of electrons and beta particles

The process by which electrons slow down and stop in material is characterized by variables which exhibit relatively large variations about mean values. For example, electrons spread out in transverse directions as they penetrate material, and electron energy losses and ranges are characterized by relatively large variations about the corresponding mean values of energy loss or range.

The stopping powers tabulated below (taken from L. Pages et al. (1972) Atomic Data, 4, 1) are made up of two components, the collision stopping power representing energy losses due to collisions with atomic electrons, and the radiation stopping power representing energy losses due to bremsstrahlung interactions. The radiation stopping power is more important for higher electron energies and higher atomic numbers of materials being penetrated. The ranges tabulated below (also taken from Pages) have been computed in the continuous slowing-down approximation (CSDA), i.e. the range is considered to be the distance along the path travelled by an ‘average electron’ until the electron stops. Few electrons reach a distance into the material equal to the CSDA range measured along the direction of initial incidence of the electron on the material.

Energy (MeV)	Be				Al
	Stopping power (MeV m² kg⁻¹)			Range (kg m⁻²)	Stopping power (MeV m² kg⁻¹)			Range (kg m⁻²)
	collision	radiation	total	Range (kg m⁻²)	collision	radiation	total	Range (kg m⁻²)

0.01	1.88 10⁰	2.44 10⁻⁴	1.88 10⁰	2.65 10⁻³	1.64 10⁰	8.53 10⁻⁴	1.64 10⁰	3.05 10⁻³
0.03	8.00 10⁻¹	2.39 10⁻⁴	8.00 10⁻¹	2.08 10⁻²	7.25 10⁻¹	8.31 10⁻⁴	7.26 10⁻¹	2.33 10⁻²
0.1	3.39 10⁻¹	2.61 10⁻⁴	3.39 10⁻¹	1.73 10⁻¹	3.16 10⁻¹	9.28 10⁻⁴	3.17 10⁻¹	1.88 10⁻¹
0.3	1.93 10⁻¹	3.80 10⁻⁴	1.93 10⁻¹	1.02 10⁰	1.83 10⁻¹	1.35 10⁻³	1.84 10⁻¹	1.08 10⁰
1	1.49 10⁻¹	8.75 10⁻⁴	1.50 10⁻¹	5.37 10⁰	1.46 10⁻¹	2.99 10⁻³	1.49 10⁻¹	5.55 10⁰
3	1.50 10⁻¹	2.44 10⁻³	1.53 10⁻¹	1.87 10¹	1.51 10⁻¹	7.43 10⁻³	1.58 10⁻¹	1.86 10¹
10	1.60 10⁻¹	9.68 10⁻³	1.70 10⁻¹	6.18 10¹	1.64 10⁻¹	2.82 10⁻²	1.92 10⁻¹	5.85 10¹
30	1.69 10⁻¹	3.42 10⁻²	2.03 10⁻¹	1.69 10²	1.75 10⁻¹	9.83 10⁻²	2.73 10⁻¹	1.46 10²
100	1.77 10⁻¹	1.36 10⁻¹	3.13 10⁻¹	4.44 10²	1.85 10⁻¹	3.82 10⁻¹	5.67 10⁻¹	3.20 10²

Energy (MeV)	Cu				Ta
	Stopping power (MeV m² kg⁻¹)			Range (kg m⁻²)	Stopping power (MeV m² kg⁻¹)			Range (kg m⁻²)
	collision	radiation	total	Range (kg m⁻²)	collision	radiation	total	Range (kg m⁻²)

0.01	1.33 10⁰	1.78 10⁻³	1.33 10⁰	3.77 10⁻³	8.94 10⁻¹	3.88 10⁻³	8.97 10⁻¹	5.57 10⁻³
0.03	6.07 10⁻¹	1.86 10⁻³	6.09 10⁻¹	2.81 10⁻²	4.38 10⁻¹	4.37 10⁻³	4.43 10⁻¹	3.99 10⁻²
0.1	2.71 10⁻¹	2.20 10⁻³	2.73 10⁻¹	2.21 10⁻¹	2.04 10⁻¹	5.43 10⁻³	2.10 10⁻¹	2.95 10⁻¹
0.3	1.58 10⁻¹	3.12 10⁻³	1.61 10⁻¹	1.25 10⁰	1.23 10⁻¹	7.69 10⁻³	1.31 10⁻¹	1.59 10⁰
1	1.26 10⁻¹	6.48 10⁻³	1.33 10⁻¹	6.29 10⁰	1.01 10⁻¹	1.52 10⁻²	1.17 10⁻¹	7.52 10⁰
3	1.31 10⁻¹	1.48 10⁻²	1.46 10⁻¹	2.07 10¹	1.07 10⁻¹	3.15 10⁻²	1.39 10⁻¹	2.32 10¹
10	1.44 10⁻¹	5.54 10⁻²	2.00 10⁻¹	6.15 10¹	1.21 10⁻¹	1.13 10⁻¹	2.33 10⁻¹	6.17 10¹
30	1.56 10⁻¹	1.87 10⁻¹	3.44 10⁻¹	1.38 10²	1.32 10⁻¹	3.46 10⁻¹	4.78 10⁻¹	1.21 10²
100	1.67 10⁻¹	7.24 10⁻¹	8.91 10⁻¹	2.60 10²	1.43 10⁻¹	1.37 10⁰	1.52 10⁰	2.00 10²

D.J.S. Findlay

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