Question

1. Which of the following is/are true about a specific particles spin?

a) always has a magnitude of hbar/2

b) The amount of angular momentum this type of particle naturally has.

c) is always up or down along an axis

d) you can only measure the spin a long one axis at a time

2. If 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

3. How do we know that electrons and other particles aren't spinning balls of charge?

Answer 1

Answer:

(1) Which of the following is/are true about a specific particles spin?

b) The amount of angular momentum this type of particle naturally has.

d) you can only measure the spin a long one axis at a time

Explanation:

Depending on the type of particle, the spin quantum number S will vary, for example an electron has spin 1/2, elementary particles like -meson has spin 0 and baryon has spin 3/2 etc. According to this reason, the spin of the particle is not only along up or down but also it has other orientations.

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

Explanation:

An electron has spin 1/2 then the magnitude of the spin vector is S = [s(s+1) ]^1/2 ћ

Therefore, S = [ 1/2 (1/2 +1) ] ћ = (√ 3) / 2 ћ.

Due to spin s = 1/2, the electron has two magnetic spin quantum numbers m_s = +1/2 and -1/2. So we can measure the magnitude of the spin vector only along these two orientations. But, anyway, along these two orientation the electron has same magnitude that is (√ 3) / 2 ћ due to same m_s values (+1/2 and -1/2). The sign of the m_s value does not play crucial role in finding the magnitude of the spin vector and it only gives the direction.

Hence, no option id correct and all are false.