What is the correct speed of alpha particles directed towards lead foil?

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SUMMARY

The speed of alpha particles directed towards lead foil with an energy of 2.86 MeV is calculated using the equation v = SQRT(2E/m). The correct calculation yields a speed of approximately 0.078c, but the expected answer is 0.039c, indicating a potential error in the mass used or the interpretation of the energy. The discrepancy arises from the need to account for the mass of the alpha particle, which is twice the mass of a proton. Additionally, relativistic effects may need to be considered for accurate results.

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Homework Statement


A beam of α particles with energy/particle = 2.86 MeV is directed towards lead foil.
What is the speed of the α particles?

Homework Equations


E = 1/2 mv^2
v = SQRT(2E/m)
v = SQRT((2)(2.86E+6)(1.602E-19) / (1.673E-27) ) = 23403526 m/s = 0.078c
but the ans is 0.039c which is half of the answer above. Why??


The Attempt at a Solution

 
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Did you do your calculations right? Did you use the right constants?

Punching
(2 * 2.86 MeV / (4 * (proton mass)))^(1/2) / c​
into google gives me the correct answer. (I've assumed the difference in proton and neutron masses are negligible)

Incidentally, I'm assuming you are neglecting relativistic effects?
 

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