Question 474: Atoms & Nuclei

Question

Using Bohr's model, the orbital period of electron in hydrogen atom in $n$th orbit is ( $\varepsilon_0=$ permittivity of free space, $h=$ Planck's constant, $m=$ mass of electron and $	heta=$ electronic charge)

Accepted Answer

The orbital period of revolution of electron in $n$th orbit is
$$T_n=\frac{2 \pi r_n}{v_n}$$
As, we know, $r_n=\left(\frac{h^2 \varepsilon_0}{\pi m e^2}ight) \frac{n^2}{Z}$
and $$v_n=\left(\frac{e^2}{2 h \varepsilon_0}ight) \frac{z}{n}$$
$	herefore \quad T_n=2 \pi \frac{h^2 \varepsilon_0 n^2}{\pi m e^2 Z} 	imes \frac{2 h \varepsilon_0 n}{e^2 Z}$
$$=\frac{4 \varepsilon_0^2 n^3 h^3}{m e^4 Z^2}$$
For hydrogen atom, $Z=1$
$$	herefore \quad T_n=\frac{4 \varepsilon_0^2 n^3 h^3}{m e^4}$$

Answer

$\frac{2 \varepsilon_0^2 n^3 h^3}{m e^4}$

Answer

$\frac{8 \varepsilon_0^2 n^3 h^3}{m e^4}$

Answer

$\frac{2 \varepsilon_0 n^2 h^2}{m e^4}$

Answer

$\frac{4 \varepsilon_0^2 n^3 h^3}{m e^4}$

Atoms & Nuclei

Using Bohr's model, the orbital period of electron in hydrogen atom in nth orbit is ( \varepsilon_0= permittivity of free space, h= Planck's constant, m= mass of electron and \theta= electronic charge)

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