Question

How much work is needed to assemble an atomic nucleus containing three protons (such as Be) if we model it as an equilateral triangle of side 2.00×10−15m with a proton at each vertex?

Answer 1

Answer:

3.46 x 10^(-13) Joules

Explanation:

The electrical work needed to assemble the system of three charges can be calculated by the following formula:

$W = \frac{1}{4 \pi \epsilon _0}}(\frac{q_1 q_2}{r_{12}}+\frac{q_3 q_2}{r_{23}}+\frac{q_1 q_3}{r_{13}})$

Where the variables are draw in teh attached image.

In an equilateral triangle:

r_12 = r_13 = r_23  = r

And all the charges are the same, therefore:

q1 = q2 = q3 = q

Replacing these values in the W formula:

$W = \frac{3 q^2}{4 \pi r \epsilon _0}$

Now let's evaluate this formula with

r =2.00 * 10^-15  m

q = 1.6 * 10^-19 C

$W = 3.46 \times 10^{-13} \frac{C^{2}V}{A s} = 3.46 \times 10^{-13} CV \\\\W = 3.46 \times 10^{-13} J$