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  • In Bohr theory of hydrogen atom, let <img alt="\mathrm{r}, \mathrm{v} \text{ and } \mathrm{E}" src="/latex-image/?%5Cmathrm%7Br%7D%2C%20%5Cmathrm%7Bv%7D%20%5Ctext%7B%20and%20%7D%20%5Cmathrm%7BE%7D"

In Bohr theory of hydrogen atom, let \mathrm{r}, \mathrm{v} \text{ and } \mathrm{E} be the radius of orbit, speed of electron and the total energy of the electron respectively. Which of the following quantities is proportional to the quantum number n ?

 

Option: 1

\mathrm{vr}


Option: 2

\mathrm{r^{2}E}


Option: 3

\frac{\mathrm{r}}{\mathrm{E}}


Option: 4

\frac{\mathrm{r}}{\mathrm{v}}


Answers (1)

best_answer

According to Bohr theory of hydrogen atom

\begin{aligned} & \mathrm{r \propto n^2} \\ & \mathrm{v \propto \frac{1}{n}} \\ & \mathrm{E \propto \frac{1}{n^2}} \\ & \mathrm{\therefore \quad v r \propto n} \end{aligned}

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