Q3.14 Inside the nucleus (S)

The nucleus of a titanium atom contains 22 protons and is about 8×10-15m (8 femtometres) in diameter. Calculate the electrostatic force and the gravitational force between two protons on either side of the nucleus.

So why don’t nuclei fly apart......?

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Hint

See S2.12 for a similar worked example.
 

Solution

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Solution

The charge on each proton is +e, whilst the mass of each is 1 amu (=1.66×10-27kg)

The electrostatic force:

$$F_e = \frac{1}{4 \pi \epsilon_0} \frac{e^2}{d^2} = 3.6N $$

The gravitational force:

$$F_G = G \frac{m^2}{r^2} = 2.9 \times 10^{-36} N$$

So the attractive gravitational force cannot counter the repulsive electrostatic force between the protons. Instead the protons are bound together by something (aptly) called the strong force.