In a hydrogen atom in its ground state, the first Bohr orbit has radius $r_1$. The electron's orbital speed becomes one-third when the atom is raised to one of its excited states. The radius of the orbit in that excited state is

Question

Aicharya · Accepted Answer

Velocity of electron $\begin{aligned} & \mathrm{V}_{\mathrm{n}} \propto \frac{1}{\mathrm{n}} \\ & \frac{\mathrm{~V}_{\mathrm{n}}}{\mathrm{~V}_{\mathrm{n}}^{\prime}}=\frac{\mathrm{n}_2}{\mathrm{n}_1} \\ & \frac{\mathrm{~V}_1}{\mathrm{~V}_1}=\frac{\mathrm{n}_2}{1} \\ & \therefore \quad \mathrm{n}_2=3 \\ & \operatorname{Radius~of~el~}^3 \\ & \mathrm{r}_{\mathrm{n}} \propto \mathrm{n}^2 \\ & \frac{\mathrm{r}_{\mathrm{n}}}{\mathrm{r}_{\mathrm{n}}^{\prime}}=\left(\frac{\mathrm{n}_1}{\mathrm{n}_2}\right)^2 \\ & \frac{r_1}{r_2}=\left(\frac{1}{3}\right)^2 \\ & r_2=9 r_1 \end{aligned}$
Radius of electron /

In a hydrogen atom in its ground state, the first Bohr orbit has radius $r_1$. The electron's orbital speed…

Solution