Question

There exist subatomic particles whose spin is characterized by $s=1$, rather than the $s=\frac{1}{2}$of electrons. These particles are said to have a spin of one.

a. What is the magnitude (as a multiple ofrole="math" localid="1650369219275" $♄$ ) of the spin angular momentum $S$for a particle with a spin of one?

b. What are the possible values of the spin quantum number?

c. Draw a vector diagram similar to Figure 41.13 to show the possible orientations of$\overrightarrow{S}$.

Short answer

(a) The magnitude of the spin angular momentum $S$for a particle with a spin of one is $S=1.48\times {10}^{-34}Js$.

(b) The possible values of the spin quantum number are$m_s=-1,0,or1$.

(c) Diagram of three possible orientation of $\overrightarrow{S}$.

Step-by-step solution

Part (a) Step 1 : Given Information

We have given that,

Particles spins are said to be one and spin of subatomic particles is characterized by $s=1.$We have to find the magnitude of angular momentum $S$for the particle with the spin of one.

Part (a) Step 2 : Simplification

We know that for $s=1$

localid="1650369236269" $S=\sqrt{s\left(s+1\right)}♄$$=\sqrt{2}♄$( $S$is spin angular momentum )

$\Rightarrow S=1.48\times {10}^{-34}Js.$

Part (b) Step 1 : Given Information

We have given that,

Particles spins are said to be one and spin of subatomic particles is characterized by $s=1$,We have to find the possible values of spin quantum number.

Part (b) Step 2 : Simplification

The spin quantum number is $ms{m}_s=-1,0$or$1.$

Part (c) Step 1 : Given Information.

We have given that,

Particles spins are said to be one and spin of subatomic particles is characterized by $s=1.$We have to draw a vector diagram to show possible orientation of $\overrightarrow{S.}$

Part (c) Step 2 : Simplification

The figure below shows the three possible orientations of$\overrightarrow{S.}$