Answer:
See attachment and explanation.
Explanation:
- The following question can be solved better with the help of a MATLAB program as follows. The code is given in the attachment.
- The plot of the graph is given in attachment.
- The code covers the entire spectrum of the poly-tropic range ( 1.2 - 1.6 ) and 20 steps ( cases ) have been plotted and compared in the attached plot.
The thickness of aluminium needed to stop the beam electrons, protons and alpha particles at the given dfferent kinetic energies is 1.5 x 10⁻¹⁴ m.
<h3>
Thickness of the aluminum</h3>
The thickness of the aluminum can be determined using from distance of closest approach of the particle.

where;
- Z is the atomic number of aluminium = 13
- e is charge
- r is distance of closest approach = thickness of aluminium
- k is Coulomb's constant = 9 x 10⁹ Nm²/C²
<h3>For 2.5 MeV electrons</h3>

<h3>For 2.5 MeV protons</h3>
Since the magnitude of charge of electron and proton is the same, at equal kinetic energy, the thickness will be same. r = 1.5 x 10⁻¹⁴ m.
<h3>For 10 MeV alpha-particles</h3>
Charge of alpah particle = 2e

Thus, the thickness of aluminium needed to stop the beam electrons, protons and alpha particles at the given dfferent kinetic energies is 1.5 x 10⁻¹⁴ m.
Learn more about closest distance of approach here: brainly.com/question/6426420