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

3.46 x 10^(-13) Joules

Step-by-step explanation:

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

`W = (1)/(4 \pi  \epsilon _0)}((q_1 q_2)/(r_(12))+(q_3 q_2)/(r_(23))+(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 = (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 * 10^(-13) (C^(2)V)/(A s) = 3.46 * 10^(-13) CV \\\\W = 3.46 * 10^(-13) J`