Question

F I say that an electron is a spin-1/2 particle, which of the following statement(s) is/are true?

a) The magnitude of the spin vector is 1/2

b) The magnitude of the spin vector is hbar/2

c) The magnitude of the spin vector along some axis is 1/2

d) The magnitude of the spin vector along some axis is hbar/2

Answer 1

d) The magnitude of the spin vector along some axis is hbar/2

Step-by-step explanation:

The magnitude of the spin vector is defined by the following equation:
`S=√(s(s+1))\hbar`

where s = n / 2 is the spin quantum number and n can only take positive integer values. For the electron we have
`s=(1)/(2)` and
`S=(√(3))/(2)\hbar`

On the other hand, the magnitude of S along some axis is given by:
`S_(i)=s_(i)\hbar`

with i=x,y,z. So, in this case we have:
`S_(z)=(\hbar)/(2)`