Question

Relation between principal quantum number and radius of orbit

Answer 1

Bohr Radius. Every atom has electron revolving around its nucleus in a fixed path.Bohr radius represent the mean radius of electron around the nucleus of hydrogen atom in its lowest energy level. ... For first orbit of hydrogen we have both the principle quantum number of orbit and atomic number equal to one

Answer 2

Answer:

Explanation:

Bohr's law states that the angular momentum is equal to the integral multiple of h/2Π. Mathematically, it can be written as :

Centripetal force = electrostatic force

$\dfrac{mv^2}{r}=\dfrac{1}{4\pi \epsilon_0}\dfrac{e^2}{r^2}$

$mv^2r=\dfrac{1}{4\pi \epsilon_0}e^2$.........(1)

Since, $mvr=\dfrac{nh}{2\pi}$

$m^2v^2r^2=\dfrac{n^2h^2}{4\pi^2}$............(2)

Where

v is the velocity of electron

r is the radius of orbit

n is the principal quantum number

h is Planck's constant

$r=\dfrac{nh}{2\pi mv}$

From equation (1) and (2) :

$mr=\dfrac{n^2h^2}{4\pi ^2}.\dfrac{4\pi \epsilon_0}{e^2}$

So, $r\propto n^2$

Hence, the radius of orbits is directly proportional to the square of principal quantum number.