Impact parameter of alpha particles

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Homework Statement

For alpha particles of 7.7 MeV, what impact parameter will result in a deflection of 2 degrees for a thin gold foil?

Homework Equations

impact parameter equation, b=\frac{kq_{\alpha}Q}{m_{\alpha}v^{2}}cot\frac{\theta}{2}

The Attempt at a Solution

Pretty easy, just plug and play intob=\frac{kq_{\alpha}Q}{m_{\alpha}v^{2}}cot\frac{\theta}{2}, but my textbook and instructor aren't very specific with what numbers we put in exactly. We know that mv^2 = 2KE, but as for the k, q and Q, do I just put k = 8.988x10^9, q(alpha) = 2(1.6x10^-19) and Q = 79(1.6x10^-19)?

I plugged in all of these numbers, along with theta = 2 degrees, and I get b = 2.70x10^-31 m. That seems kind of small for a deflection of 2 degrees. Did I do something wrong? Am I plugging in the wrong numbers?

Thank you all in advance.

 

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After taking a closer look, I think my problems are:

1. I need to convert MeV to eV,
2. For q(alpha), use q = 2,
3. For Q, use Q =79,
4. Multiply k*q(alpha)*Q*e for e = 1.6x10^-19.

I did this for another question for which I had the answer, and I got the correct answer. Is this the problem here? Do I always need to use the above 4 solutions to my problem?

The thing is, i was under the assumption that q = 2e, and then Q = 79e, which means you need to have e^2 in the numerator...but that is not the case...I don't get that...