Question

2 positive ions each carrying a charge q are separated by a distance d. If F is the forceof repulsion between the ions,the number of electrons missing from each ion will be ( e being the charge on electron)

1) 4 pie∈0Dd2/q²

24 pie∈0 Fd²/e²

3) ( 4 pie∈0 Fe²/d²)^1/2

4) (4 pie∈0 Fd²/e²)^1/2

Answer 1

If q is the positive charge on each ion separated by a distance 'd'.Then the Coulomb's force between the charges is given by,
$$\begin{gathered} \mathrm{F}=\frac{{\mathrm{kq}}^2}{{\mathrm{d}}^2} \\ =\frac{1}{4\mathrm{\pi }{\in }_0}\frac{{\mathrm{q}}^2}{{\mathrm{d}}^2} \\ \mathrm{or}\mathrm{q}2=\mathrm{F}\times 4\mathrm{\pi }\in \end{gathered}$$₀d² Or q=4π∈0Fd2 Now, q=ne where, n=number of electrons and e=charge on electron So, n=q/e =4π∈0Fd2e or n=4π∈0Fd2/e2