Question

An electron is moving round the nucleus of hydrogen atom in a circular orbit of radius. The coulomb force F between the two is?

• A. $k\frac{e^2}{r^3}\overrightarrow{r}$
• B. $-k\frac{e^2}{r^3}\overrightarrow{r}$
• C. $k\frac{e^2}{r^2}\overrightarrow{r}$
• D. $-k\frac{e^2}{Ar}$

Answer 1

The correct option is B $-k\frac{e^2}{r^3}\overrightarrow{r}$

Using Coulomb's law, the force between two charges is given by,

$\overrightarrow{F}=k\frac{q_1{q}_2}{r^3}\overrightarrow{r}$ where $r=$ distance between charges.

Here, $q_1=-e$, charge of an electron ; $q_2=Ze=e$, charge of the nucleus and $r=$ radius of hydrogen atom.

(note: for a hydrogen atom, atomic number $=Z=1$)

Thus, the force between electron and nucleus will be, $F=k\frac{(-e)e}{r^3}\overrightarrow{r}=-k\frac{e^2}{r^3}\overrightarrow{r}$