Question 298: Magnetism and Matter

Question

An electron in a hydrogen atom revolves around its nucleus with a speed of $6.76 	imes 10^6 \mathrm{~ms}^{-1}$ in an orbit of radius $0.52 \mathrm{~A}^{\circ}$. The magnetic field produced at the nucleus of the hydrogen atom is _________ T.

Accepted Answer

The formula for the magnetic field due to a moving charge is given by:
$\mathbf{B}=\frac{\mu_0}{4 \pi} \frac{q v \sin 	heta}{r^2}$
where $\mu_0$ is the permeability of free space, $q$ is the charge of the moving particle, $v$ is the speed of the particle, $	heta$ is the angle between the velocity vector and the position vector from the particle to the point where we want to calculate the magnetic field, and $r$ is the distance between the particle and the point where we want to calculate the magnetic field.
In this case, we're interested in the magnetic field produced by the electron moving in a circular orbit around the nucleus of a hydrogen atom. Since the orbit is circular, the angle between the velocity vector and the position vector is 90 degrees, so $\sin 	heta = 1$. We can substitute the known values into the formula to find the magnetic field:
$\mathbf{B}=\frac{\mu_0}{4 \pi} \frac{q v \sin 	heta}{r^2} = \frac{\mu_0}{4 \pi} \frac{e v}{r^2}$
where $e$ is the charge of an electron. We know that the radius of the orbit is $0.52 \mathrm{~A}^{\circ}$, which is equivalent to $0.52 	imes 10^{-10} \mathrm{m}$.
Substituting the values, we get:
$\mathbf{B}=\frac{\mu_0}{4 \pi} \frac{e v}{r^2} =\frac{10^{-7} 	imes 1.6 	imes 10^{-19} 	imes 6.76 	imes 10^6}{0.52 	imes 0.52 	imes 10^{-20}} =  40 ~\mathrm{T}$
This means that the magnetic field produced by the electron moving in a circular orbit around the nucleus of a hydrogen atom is 40 tesla, which is an incredibly strong magnetic field.

Magnetism and Matter

An electron in a hydrogen atom revolves around its nucleus with a speed of 6.76 \times 10^6 \mathrm{~ms}^{-1} in an orbit of radius 0.52 \mathrm{~A}^{\circ}. The magnetic field produced at the nucleus of the hydrogen atom is _________ T.

Integer / Numeric Answer Type