Question

The equation is given by Bohr to calculate the radius of the ‘nth orbit of the hydrogen atom is

• A. $r_n=\frac{n^2{h}^2}{4{\pi }^{2}me}$
• B. $r_n=\frac{n^2{h}^2}{4{\pi }^2{me}^2}$
• C. $r_n=\frac{{nh}^2}{4{\pi }^{2}me}$
• D. $r_n=\frac{n^2{h}^2}{4{\pi }^2{m}^{2}e}$

Answer 1

The correct option is B

${\mathrm{r}}_{\mathrm{n}}=\frac{{\mathrm{n}}^2{\mathrm{h}}^2}{4{\mathrm{\pi }}^2{\mathrm{me}}^2}$

${\mathrm{r}}_{\mathrm{n}}=\frac{{\mathrm{n}}^2{\mathrm{h}}^2}{4{\mathrm{\pi }}^2{\mathrm{Zme}}^2}$is the equation to calculate the radius of the nth orbit of the hydrogen atom.

where h= Planck's constant(6.625x10^-34Js),

n= number of orbits

m= mass of an electron(9.1 x 10^-28g)

e= charge of electron(1.6x 10^-19C)

Z=1 for hydrogen.

By placing all these values, an Equation to calculate the radius of the nth orbit of the hydrogen atom ${\mathrm{r}}_{\mathrm{n}}=\frac{{\mathrm{n}}^2{\mathrm{h}}^2}{4{\mathrm{\pi }}^2{\mathrm{me}}^2}$

$\left({\mathrm{r}}_{\mathrm{n}}\right)=0.529\times {\mathrm{n}}^2\mathrm{angstrom}$.

Conclusion Statement: Option (b) is the correct answer.