According to the Bohr theory of hydrogen atom, the speed of the electron, its energy and the radius of its orbit varies with the principal quantum number n, respectively, as

Question

According to the Bohr theory of hydrogen atom, the speed of the electron, its energy and the radius of its orbit varies with the principal quantum number n, respectively, as (A) (1/n), (1/n2), n2 (B) (1/n), n2, (1/n2) (C) n2, (1/n2), n2 (D) n, (1/n2), (1/n2)

Tardigrade Admin · Accepted Answer

According to Bohr's theory of hydrogen atom
(i) The speed of electron in

n

th orbit

v_{n} = \frac{Z e ^{2}}{2 ε _{0} nh}

or

v_{n} \propto \frac{1}{n}

(ii) The energy of electron in the

n

th orbit

E_{n} = - (\frac{m e ^{4}}{8 ε _{0}^{2} h ^{2}}) \cdot \frac{Z ^{2}}{n ^{2}}

= - 13.6 \frac{Z ^{2}}{n ^{2}} e V

or

E_{n} \propto \frac{1}{n ^{2}}

(iii) The radius of the electron in the

n

th orbit

r_{n} = \frac{n ^{2} h ^{2} ε _{0}}{πm Z e ^{2}} = 0.53 \frac{n ^{2}}{2} \overset{˚}{A}

r_{n} \propto n^{2}

Q. According to the Bohr theory of hydrogen atom, the speed of the electron, its energy and the radius of its orbit varies with the principal quantum number n, respectively, as

$\frac{1}{n}, \frac{1}{n ^{2}}, n^{2}$

$\frac{1}{n}, n^{2}, \frac{1}{n ^{2}}$

$n^{2}, \frac{1}{n ^{2}}, n^{2}$

$n, \frac{1}{n ^{2}}, \frac{1}{n ^{2}}$

Q. According to the Bohr theory of hydrogen atom, the speed of the electron, its energy and the radius of its orbit varies with the principal quantum number n, respectively, as

n1​,n21​,n2

n1​,n2,n21​

n2,n21​,n2

n,n21​,n21​

$\frac{1}{n}, \frac{1}{n ^{2}}, n^{2}$

$\frac{1}{n}, n^{2}, \frac{1}{n ^{2}}$

$n^{2}, \frac{1}{n ^{2}}, n^{2}$

$n, \frac{1}{n ^{2}}, \frac{1}{n ^{2}}$