Question

Derive an expression for the velocity of an electron revolving round the nucleus in the orbit of hydrogen atom. ​

Answer 1

$\mathfrak{\huge{\underline{\underline{Answer}}}}$

From Bohr postulate, we have,

$\frac{mv}{r} = \frac{ {ze}^{2} }{4\pi \: e0 {r}^{2} } = > (1)$

z -------> atomic number

m ------> mass of electron

r --------> radius of orbit

$mvr = \frac{nh}{2\pi} = > (2)$

and

Dividing (1) by (2):

$= > v = ( \frac{ {ze}^{2} }{4\pi \: e0} ) \frac{2\pi}{n} = \frac{ {ze}^{2} }{4\pi \: e0h}$

Thus, velocity of electron in nth

$permitted \: orbit \: i s \: {v}^{n} = \: \frac{ze}{4\pi \: e0h}$