In the n th orbit of hydrogen atom, ratio of its radius and de-Broglie wavelength associated with it, is:

Question

In the n th orbit of hydrogen atom, ratio of its radius and de-Broglie wavelength associated with it, is: (A)  (1/2π n)  (B)  (1/2π n2)  (C)  (n/2π )  (D)  (n2/2π )

Tardigrade Admin · Accepted Answer

The velocity of electron in nth orbit is given by v=(n h/2 π m rn) Also, λ=(h/p)=(h/m v) From eqs. (1) and (2), we have λ =(h/m (n h)2 π m rn) =(2 π rn/n) ∴ (rn/λ) =(n/2 π)

Q. In the $n$ th orbit of hydrogen atom, ratio of its radius and de-Broglie wavelength associated with it, is:

$\frac{1}{2 πn}$

$\frac{1}{2 π n ^{2}}$

$\frac{n}{2 π}$

$\frac{n ^{2}}{2 π}$

The velocity of electron in $n$ th orbit is given by
$v = \frac{nh}{2 πm r _{n}}$
Also, $λ = \frac{h}{p} = \frac{h}{m v}$
From eqs. (1) and (2), we have
$λ = \frac{h}{m \frac{nh}{2 πm r _{n}}}$
$= \frac{2 π r _{n}}{n}$
$∴ \frac{r _{n}}{λ} = \frac{n}{2 π}$

Q. In the n th orbit of hydrogen atom, ratio of its radius and de-Broglie wavelength associated with it, is:

2πn1​

2πn21​

2πn​

2πn2​