Final answer:
The radius of the electron's circular path in a magnetic field can be determined using its angular momentum, the known mass and charge of an electron, and the magnetic force equation, enabling us to solve for both the electron's velocity and the radius of its path.
Step-by-step explanation:
To determine the radius of the circular path an electron follows in a magnetic field, we can use the relationship between angular momentum (L), the magnetic field (B), and the radius (r). The angular momentum of an electron moving in a magnetic field is given by L = mvr, where m is the mass of the electron, v is its velocity, and r is the radius of the circular path.
Given that the angular momentum L is 6.00 × 10^-25 J·s and the mass of an electron m is 9.11 × 10^-31 kg, we can rearrange the equation to r = L / (mv). However, we need to determine the velocity v of the electron to find r.
The electron's centripetal force necessary to maintain its circular motion is provided by the magnetic force, which is given by F = qvB, where q is the charge of the electron, v is the velocity, and B is the magnetic field.
We also know that the centripetal force is F = (mv^2)/r. Setting qvB equal to (mv^2)/r and substituting q for the known charge of an electron allows us to solve for v and subsequently for r. After finding the velocity, we can finally determine the radius of the circular path from the provided angular momentum.