Question

Suppose a hydrogen atom was somehow enlarged so that the nucleus has a diameter of 10 cm. What is the diameter of the volume occupied by the orbit of the electron in the planetary model? Assume that the radius of the nucleus (a proton) is 1 fm (1 × 10−15 m) and the radius of a hydrogen atom is 5 × 10−11 m

Answer 1

Actual radius of necleus, R_nucleus = 1*10^-15 m
Actual radius of orbit of electron, R_orbit = 5*10^-11 m

Enalrged radius of necleus, R_nucleus' = 10 cm/2 = 5 cm

Enlarged radius of orbit of electron, R_orbit' = ?

R_orbit'/R_nculeus' = R_orbit/R_nculeus

R_orbit/5 = 5*10^-11/(1*10^-15)

R_orbit = 5*5*10^4 cm

= 25*10^4 cm

= 25*10^2 m

= 2500 m

diameter of orbit = 2*R_orbit

= 2*2500

= 5000 m (or) 5.0*10^3 m <<<<<<<<<----------------Answer