Question

A normal hydrogen atom consist of a proton nucleus and oribital electron , each carrying a charge (e).assuming that the electron orbit is circular and the seperation between the particles is 5.3×10^-11m.find

(I) the force of electrical attraction between the particles

(II) the electron oribital speed

Answer 1

Given:

$r=5.3×10^{-11}\:\rm m$

$e=1.6×10^{-19}\:\rm C$

$m=9.1×10^{-31}\:\rm kg$

(I) the force of electrical attraction between the particles

$$F=k\frac{e^2}{r^2}=9*10^9\frac{(1.6*10^{-19})^2}{(5.3×10^{-11})^2}=8.2*10^{-6}\: \rm N$$

(II) the electron oribital speed

$$F=\frac{mv^2}{r}$$

$$v=\sqrt{\frac{Fr}{m}}=\sqrt{\frac{8.2*10^{-6}*5.3×10^{-11}}{9.1×10^{-31}}}=2.2*10^7\:\rm m/s$$