Ok, let\'s use the following information to very roughly estimate the size of th

Question

Ok, let's use the following information to very roughly estimate the size of the nucleus. Rutherford, Geiger, and Marsden (his students) fired a beam of alpha particles at a gold foil. The alpha particles had an energy of about 3.6 million electron volts, a charge of +2e, and a mass of about four AMU (one Atomic Mass Unit is 1.66 x 10-27 kg. Gold has atomic number 79.
How close could the alpha particles get to the gold nucleus? This is our rough estimate of the nuclear size.
Enter the answer in units of femtometers.
Penalty factor 0.1

Explanation / Answer

Energy must be conserved and when the alpha particle is fired it will have KE. All of the KE will be transferred to PE at its closest point, so

KE is Given as 3.6 million Electron Volts

Electric PE = kqq/r

So

3.6 MeV = kqq/r

Since 1eV = 1.6 X 10-19 J, the energy is 5.76 X 10-13 J

5.76 X 10-13 J = kqq/r

So r = kqq/5.76 X 10-13

The q for the alpha particle is 2e

The q for the gold nucleus is 79e (The Atomic Number of Gold is 79)

r = (9 X 109)(2)(1.6 X 10-19)(79)(1.6 X 10-19)/(5.76 X 10-13)

r = 6.32 X 10-14 m = 63.2 fm

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