In a hydrogen-like species, the net force acting on a revolving electron in an orbit as given by the Bohr model is proportional to [ n arrow principal quantum number, Z arrow atomic number]

Question

In a hydrogen-like species, the net force acting on a revolving electron in an orbit as given by the Bohr model is proportional to [ n arrow principal quantum number, Z arrow atomic number] (A) (Z3/n4) (B) (n3/Z2) (C) (Z2/n3) (D) (n4/Z3)

Tardigrade Admin · Accepted Answer

The net force on a revolving electron is

F = \frac{m v ^{2}}{r}

F \propto \frac{v _{n}^{2}}{r _{n}}

The velocity of the electron in the

n^{t h}

shell

v_{n} \propto \frac{Z}{n}

and the radius of the

n^{t h}

shell

r_{n} \propto \frac{n ^{2}}{Z}

\Rightarrow F \propto \frac{Z ^{3}}{n ^{4}}

Q. In a hydrogen-like species, the net force acting on a revolving electron in an orbit as given by the Bohr model is proportional to [ $n \to$ principal quantum number, $Z \to$ atomic number]

$\frac{Z ^{3}}{n ^{4}}$

$\frac{n ^{3}}{Z ^{2}}$

$\frac{Z ^{2}}{n ^{3}}$

$\frac{n ^{4}}{Z ^{3}}$

The net force on a revolving electron is
$F = \frac{m v ^{2}}{r}$
$F \propto \frac{v _{n}^{2}}{r _{n}}$
The velocity of the electron in the $n^{t h}$ shell
$v_{n} \propto \frac{Z}{n}$
and the radius of the $n^{t h}$ shell
$r_{n} \propto \frac{n ^{2}}{Z}$
$\Rightarrow F \propto \frac{Z ^{3}}{n ^{4}}$

Q. In a hydrogen-like species, the net force acting on a revolving electron in an orbit as given by the Bohr model is proportional to [ n→ principal quantum number, Z→ atomic number]

n4Z3​

Z2n3​

n3Z2​

Z3n4​

The net force on a revolving electron is F=rmv2​ F∝rn​vn2​​ The velocity of the electron in the nth shell vn​∝nZ​ and the radius of the nth shell rn​∝Zn2​ ⇒F∝n4Z3​

Q. In a hydrogen-like species, the net force acting on a revolving electron in an orbit as given by the Bohr model is proportional to [ $n \to$ principal quantum number, $Z \to$ atomic number]

$\frac{Z ^{3}}{n ^{4}}$

$\frac{n ^{3}}{Z ^{2}}$

$\frac{Z ^{2}}{n ^{3}}$

$\frac{n ^{4}}{Z ^{3}}$