While obtaining the Bohr radius for the ground state of hydrogen

CHEMISTRY · Single correct · CBSE · Chemistry · Structure of Atom · Structure of Atom

Problem

While obtaining the Bohr radius for the ground state of hydrogen, the speed obtained from the quantisation condition

v = \dfrac{\hbar}{mr}

is substituted in the force balance equation. Which of the following relations is then obtained? (a)

\dfrac{e^{2}}{\varepsilon_{0} r^{2}} = \dfrac{\hbar^{2}}{m r^{3}}

(b)

\dfrac{e^{2}}{4\pi\varepsilon_{0} r^{2}} = \dfrac{h^{2}}{m r^{3}}

(c)

\dfrac{e^{2}}{4\pi\varepsilon_{0} r^{2}} = \dfrac{\hbar^{2}}{m r^{3}}

(d)

\dfrac{e^{2}}{4\pi\varepsilon_{0} r^{2}} = \dfrac{4\hbar^{2}}{m r^{3}}