Question

what do you mean by integer 'Spin' ?

Answer 1

In quantum mechanics, the spin of a particle (which quantum mechanics being what it is, is not actually spinning, but something analogous to spin), is quantised. This means that it can only take on specific values of spin, in units of Planck's constant. When we talk about integer then we mean that we can have \(1\hbar\), \(2\hbar\), \(3\hbar\) etc up to \(n\hbar\), With \(n\) are integer numbers (integers being whole numbers). These types of particles with integer spin are known as Bosons, and obey Bose-Einstein Statistics.

Conversely there is a a type of particle that can only have half integer spin, called fermions. What this means is that the particles can only have spins of \(\frac{1}{2}\hbar\), \(\frac{3}{2}\hbar\), \(\frac{5}{2}\hbar\), etc up to \(\frac{n}{2}\hbar\), where \(n\) is an odd integer number number.

So the general form for all particles is that they will have a spin value of \(\frac{n}{2}\hbar\), where \(n\) can take the values of 0, \(\pm\)1, \(\pm\)2, \(\pm\)3 etc and if n is even it is a boson since the spin ends up as an integer number of Planck's constant, and if n is odd then it is a fermion, since the spin ends up having half integer values of Planck's constant. No other values for spin are permitted (i.e. (2/3 or 5/4 etc).