Question

A magnesium ion, Mg2+, with a charge of 3.2×10−19C and an oxide ion, O2−, with a charge of −3.2×10−19C, are separated by a distance of 0.25 nm. How much work would be required to increase the separation of the two ions to an infinite distance?

Answer 1

Explanation:

Formula for work done is as follows.

           W = $-k \frac{q_{1}q_{2}}{d}$    

where,  k = proportionality constant = $8.99 \times 10^{9} Jm/C^{2}$

            $q_{1} = charge of Mg^{2+} = 3.2 \times 10^{-19} C$

            $q_{2} = charge of O_{2-} = -3.2 \times 10^{-19} C$

            d = separation distance = 0.45 nm = $0.45 \times 10^{-9} m$

Now, we will put the given values into the above formula and calculate work done as follows.

         W = $-k \frac{q_{1}q_{2}}{d}$    

           = $\frac{-[8.99 \times 10^{9} Jm/C^{2} \times 3.2 \times 10^{-19} C \times -3.2 \times 10^{-19} C]}{0.25 \times 10^{-9} m}$  

           = $3.68 \times 10^{-18} J$

Thus, we can conclude that work required to increase the separation of the two ions to an infinite distance is $3.68 \times 10^{-18} J$.