Orbital Magnetic Dipole Moment of the Electron

Find the magnitude of the orbital magnetic dipole moment of the electron in the 3 p state.

(Express your answer in terms of \(\mu_{\mathrm{B}}\).)

Text Transcription:

mu B

Lecture 3 VECTORS In 1 dimension, we use + or – to indicate direction of a vector In 2 or 3D we need more than just a sign to indicate direction, such as an angle We express vectors as arrows, there the tail of the arrow is where the vector starts and the tip is where it ends. The length of the arrow represents the magnitude of the vector and the direction of the arrow represents the orientation of the vector Ay A Ax = Acosϴ Ay = Asin ϴ A = √Ax^2 = Ay^2 Ax Unit vector of a = (Axi + Ayj + Azk) position r = xi + yj + zk length r = √x^2 + y^2 + z^2 unit vector = x/r + y/r +z/r **If we have a magnitude for the resultant (Force , length, etc.), we can multiply that magnitude by the unit vector to get the (Force, length, etc.) of each component Vector Addition (tip to tail) C b C = a + b By putting a and b tip to tail, we a connect a’s tail with b’s tip to get the sum of the vectors (C) **Note: To subtract vectors just flip one vector’s direction and add like above. Ex: A – B = A + B To add 2 or more vectors mathematically, simply decompose each vector into its x, y, and z components and add like terms (x’s with x’s etc.) This will give you the components of the resultant. To get the total resultant, do