Question

If in Bohr's atomic model, it is assumed that force between electron and proton varies inversely as r4 energy of the system will be proportional to

Answer 1

answer : energy of the system is inversely proportional to r³.


explanation : a/c to question, force between electron and proton varies inversely as r⁴.

e.g., $F\propto\frac{1}{r^4}$

or, $F=\frac{K}{r^4}$, where K is proportionality constant.

according to Bohr's atomic model, electrostatic force is balanced by centripetal force.

so, $\frac{mv^2}{r}=\frac{K}{r^4}$

or, $\frac{1}{2}mv^2=\frac{K}{2r^3}$

hence, kinetic energy is inversely proportional to r³.

again, Potential energy = -Kinetic energy/2

so, potential energy is also inversely proportional to r³.

so, energy of the system (P.E + K.E) is also inversely proportional to r³.