If an electron is revolving around the hydrog | vedclass

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

Question

(D) The electrostatic force between the nucleus and the electron provides the necessary centripetal force for circular motion.Electrostatic force $=$

Vedclass · Accepted Answer

$1.59 	imes 10^{6} \,ms^{-1}$

Vedclass · Answer

(D) The electrostatic force between the nucleus and the electron provides the necessary centripetal force for circular motion.Electrostatic force $=$ Centripetal force$\frac{1}{4 \pi \varepsilon_{0}} \frac{Z e^{2}}{r^{2}} = \frac{m v^{2}}{r}$Solving for velocity $v$:$v = \sqrt{\frac{1}{4 \pi \varepsilon_{0}} \frac{Z e^{2}}{m r}}$Given values: $Z = 1$, $e = 1.6 	imes 10^{-19} \,C$, $r = 0.1 	imes 10^{-9} \,m$, $m = 9.1 	imes 10^{-31} \,kg$, and $\frac{1}{4 \pi \varepsilon_{0}} = 9 	imes 10^{9} \,N \cdot m^{2} \cdot C^{-2}$.Substituting these values:$v = \sqrt{\frac{9 	imes 10^{9} 	imes 1 	imes (1.6 	imes 10^{-19})^{2}}{9.1 	imes 10^{-31} 	imes 0.1 	imes 10^{-9}}}$$v = \sqrt{\frac{9 	imes 10^{9} 	imes 2.56 	imes 10^{-38}}{9.1 	imes 10^{-41}}}$$v = \sqrt{\frac{23.04 	imes 10^{-29}}{9.1 	imes 10^{-41}}} = \sqrt{2.53 	imes 10^{12}} \approx 1.59 	imes 10^{6} \,ms^{-1}$.

If an electron is revolving around the hydrogen nucleus at a distance of $0.1 \,nm$, what should be its speed?

Similar Questions

In a hydrogen atom,the binding energy of the electron in the $n^{th}$ state is $E_n$. Then,the frequency of revolution of the electron in the $n^{th}$ orbit is:

To explain his theory,Bohr used

$A$ sample of hydrogen-like atoms produces an emission spectrum consisting of $10$ wavelengths arising from all possible transitions. During this process,the maximum angular momentum change for an electron transitioning from a higher energy level to a lower energy level is:

According to Bohr's model, the highest kinetic energy is associated with the electron in the

In the hydrogen atom, the radii of the first four Bohr orbits are related as:

Vedclass Test Series

Exam Paper Generator

Online Exam Module