Consider classical electron orbit with radius 53pm (picometers) that has a magnetic moment equal to 2μB (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 equation relating magnetic moment to current and the radius of the orbit.
The equation is:
magnetic moment (μ) = (current (I) * Area (A) * number of turns (N)) / 2
Here, the number of turns (N) is 1 since we are considering a single electron and the area (A) is the area of the circular orbit, which can be calculated using the formula for the area of a circle: A = π * r^2, where r is the radius of the orbit.
Let's plug in the values and solve for the current (I):
Given:
magnetic moment (μ) = 2μB (Bohr magneton)
radius (r) = 53 pm (picometers) = 53 * 10^-12 meters
We need to convert the radius to meters to have consistent units with the equation. So, 53 pm = 53 * 10^-12 meters.
Using the formula for the area of a circle: A = π * r^2, we get:
A = π * (53 * 10^-12)^2
Next, we rearrange the equation for current (I):
I = (2 * μ * 2) / (A * N)
Now, substitute the given values into the equation:
I = (2 * 2μB) / (π * (53 * 10^-12)^2 * 1)
Finally, calculate the current (I) using the provided values.