Give the relationship between orbital radius and velocity of an electron for a hydrogen atom.
(N/A) According to Bohr's theory of the hydrogen atom,the electrostatic force between the nucleus and the electron provides the necessary centripetal force for circular motion:
$F_e = F_c$
$\frac{1}{4\pi\epsilon_0} \cdot \frac{e^2}{r^2} = \frac{mv^2}{r}$
From this,we can derive the relationship between the orbital radius $r$ and the velocity $v$ of the electron:
$\frac{1}{4\pi\epsilon_0} \cdot \frac{e^2}{r} = mv^2$
Thus,the relationship is $r = \frac{e^2}{4\pi\epsilon_0 mv^2}$.
$F_e = F_c$
$\frac{1}{4\pi\epsilon_0} \cdot \frac{e^2}{r^2} = \frac{mv^2}{r}$
From this,we can derive the relationship between the orbital radius $r$ and the velocity $v$ of the electron:
$\frac{1}{4\pi\epsilon_0} \cdot \frac{e^2}{r} = mv^2$
Thus,the relationship is $r = \frac{e^2}{4\pi\epsilon_0 mv^2}$.
Explore More
Similar Questions
Hydrogen $(_1H^1)$,Deuterium $(_1H^2)$,singly ionized Helium $(_2He^4)^+$,and doubly ionized Lithium $(_3^6Li)^{++}$ all have one electron around the nucleus. Consider an electron transition from $n = 2$ to $n = 1$. If the wavelengths of emitted radiation are $\lambda_1, \lambda_2, \lambda_3$,and $\lambda_4$ respectively,then approximately which one of the following is correct?
Energy levels $A, B, C$ of a certain atom correspond to increasing values of energy,i.e.,$E_A < E_B < E_C$. If $\lambda_1, \lambda_2, \lambda_3$ are the wavelengths of radiations corresponding to the transitions $C$ to $B$,$B$ to $A$,and $C$ to $A$ respectively,which of the following statements is correct?
MediumAIIMS 1995
View SolutionChoose the correct statement$(s)$ for hydrogen and deuterium atoms (considering the motion of the nucleus).
Medium
View SolutionThe de-Broglie wavelength associated with an electron of a hydrogen atom in its ground state is (in $\text{ Å}$)
DifficultKCET 2020
View SolutionIn which of the following systems will the radius of the first orbit $(n = 1)$ be minimum?
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo