Consider classical electron orbit with radius
53pm (picometers) that has a magnetic moment equal to sqrt(2)*μB (the Bohr magneton). What is the current of that orbiting electron in A?
To determine the current of the orbiting electron, we need to use the formula relating the magnetic moment of the electron to the orbital radius and the current. The formula is given as:
magnetic moment = (current * area enclosed by the orbit) / (2 * π)
The magnetic moment of the electron is given as sqrt(2) * μB, where μB represents the Bohr magneton. The area enclosed by the orbit can be calculated as the area of a circle with radius r.
Let's plug in the values into the formula and solve for the current.
The orbital radius, given as 53 picometers, can be converted to meters by dividing by 10^12 (since 1 picometer = 10^(-12) meters).
r = 53 pm / (10^12 m/picometer)
r = 53 * 10^(-12) meters
The formula becomes:
sqrt(2) * μB = (current * π * r^2) / (2 * π)
Simplifying the formula by canceling out the π:
sqrt(2) * μB = (current * r^2) / 2
Let's rearrange the equation to solve for the current:
current = (2 * sqrt(2) * μB) / r^2
Now we can substitute the known values:
current = (2 * sqrt(2) * μB) / (53 * 10^(-12))^2
The value of the Bohr magneton μB is approximately 9.274 x 10^(-24) A*m^2.
current = (2 * sqrt(2) * 9.274 x 10^(-24) A*m^2) / (53 * 10^(-12))^2
Evaluating the expression, we can calculate the current of the electron orbit.