In the Bohr model of the hydrogen atom,the fo | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) According to Coulomb's law,the electrostatic force $F$ between the nucleus and the electron is given by $F = \frac{1}{4\pi\epsilon_0} \frac{Ze^2}{

Vedclass · Accepted Answer

$F \propto 1/n^4$

Vedclass · Answer

(B) According to Coulomb's law,the electrostatic force $F$ between the nucleus and the electron is given by $F = \frac{1}{4\pi\epsilon_0} \frac{Ze^2}{r^2}$.Since $F \propto \frac{1}{r^2}$,we need to find the relationship between the radius $r$ and the principal quantum number $n$.In the Bohr model,the radius of the $n$-th orbit is given by $r_n \propto n^2$.Substituting this into the force expression: $F \propto \frac{1}{(n^2)^2} = \frac{1}{n^4}$.Therefore,the force on the electron is proportional to $1/n^4$.

In the Bohr model of the hydrogen atom,the force on the electron is proportional to which power of the principal quantum number $n$?

Similar Questions

The radius of a certain orbit of a hydrogen atom is $8.48 \mathring{A}$. If the energy of the electron in this orbit is $E/x$,then $x = . . . .$
(Given $a_0 = 0.529 \mathring{A}$,$E =$ energy of the electron in the ground state)

$(a)$ Using the Bohr model,calculate the speed of the electron in a hydrogen atom in the $n = 1, 2,$ and $3$ levels.
$(b)$ Calculate the orbital period in each of these levels.

Minimum excitation potential of Bohr's first orbit in hydrogen atom is.....$V$

In any Bohr orbit of the hydrogen atom,the ratio of kinetic energy to potential energy of the electron is

For an electron moving in the $n^{th}$ orbit of an $H$-atom,the angular velocity is proportional to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module