Question

How much work is required to bring three protons, initially infinitely far apart, to a configuration where each proton is 1.5×10−15m from the other two? (This is a typical separation for protons in a nucleus.) Express your answer using two significant figures.

Answer 1

Answer:

$W=46.08\times 10^{-14}J$

Explanation:

The work done(W) in bringing 2 protons to a separation 'r' is given as:

$W=\frac{kq^2}{r}$

where,

k= coulomb's constant = 9 × 10⁹ N

q = charge of protons = 1.6 × 10⁻¹⁹ C

Now, the third charge (or proton) is brought near the other two  protons

Thus, work done against both these is

$W_2+W_3=\frac{kq^2}{r}+\frac{kq^2}{r}$

Now,

The total work done (W) = $W_1 +W_2+W_3=3\frac{kq^2}{r}$

or

$W=3\times \frac{9\times 10^9\times (1.6\times 10^{-19})^2}{1.5\times 10{-15}}$

or

$W=46.08\times 10^{-14}J$