The subatomic omega particle has spin s=32. What angles might its intrinsic angular in momentum vector make with the z-axis?

Short Answer

Expert verified

Angles that intrinsic angular momentum vector39.2°,75°,105°and140.8°

Step by step solution

01

Given information: 

s=32

02

Concept of angular momentum:

Following formula is used to calculate projection of spin angular moment with respect to z-axis,cosθ=Sz|S| Angular momentum along z-axis is,Sz=msh spin angular momentum vector's magnitude is|S|=S(S+1)h2.

03

Evaluate the spin angular momentum

The omega particle has spin 32. Its components of angular momentum along the z-axis are therefore Sz=msh.

For mz=32,12,+12,+32

The magnitude of its spin angular momentum vector is calculated by substituting 32for S in the equation |S|=S(S+1)h2as follows.

|S|=S(S+1)2=3232+12=154h

The possible angles with respect to the z-axis are shown in the diagram.

Formz=32the angle is equal to

cosθ=Sz|S|=32h154h2=315=0.77460θ=39.2°

For mz=12the angle is equal to

cosθ=Sz|S|=12h154h2=115=0.25820θ=75.0°

For mz=12the angle is equal to

cosθ=S2|S|=12h154h2=0.25820θ=105°

For mz=32 the angle is equal to

cosθ=Sz|S|=32h154h2=315=0.77460θ=140.8°

Therefore, Angles that intrinsic angular momentum vector 39.2°,75°,105°and140.8°.

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