# Help With Finding The Speed of an Alpha Particle

Hey guys, I am having a hard time solving for this problem, and I can’t seem to figure out what I am doing wrong.

1. The problem statement, all variables and given/known data

In the form of radioactive decay known as alpha decay, an unstable nucleus emits a helium-atom nucleus, which is called an alpha particle. An alpha particle contains two protons and two neutrons, thus having mass m=4u and charge q=2e. Suppose a uranium nucleus with 92 protons decays into thorium, with 90 protons, and an alpha particle. The alpha particle is initially at rest at the surface of the thorium nucleus, which is 15 fm in diameter.

What is the speed of the alpha particle when it is detected in the laboratory? Assume the thorium nucleus remains at rest.

2. Relevant equations

K[itex]_{}f[/itex]+qV[itex]_{}f[/itex] = K[itex]_{}i[/itex]+qV[itex]_{}i[/itex]

V = KQ/R

e=1.6*10^-19

3. The attempt at a solution

K[itex]_{}f[/itex] + 0 = 0 + qV[itex]_{}i[/itex]

1/2MV^2 = q(KQ/R)

R = 1.5*10^-14m

K = 8.99*10^9

Q = 90(1.6*10^-19)

q = 2e

m = 4u

2V^2 = 8630400

V^2 = 4315200

V = 2077.31

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