Quarks have spin12 The baryons protons neutrons arc hound st

Quarks have spin-1/2. The baryons (protons, neutrons,...) arc hound states of three quarks. Mesons (pious, kaons,...) are hound states of a quark and an antiquark. Assume that the quarks are bound in states of zero orbital angular momentum. What are the possible spins for mesons? What are the possible spins for baryons?

Solution

(1) S₁=1/2   and S₂= 1/2 this means S can take values 0 or 1 (for mesons )

(2) S₁=1/2, S₂=1/2 and S₃=1/2

first we add S₁=1/2   and S₂= 1/2 ,so S₁₂ =0 or 1

now we add the third spin S₃ =1/2

S₁₂ =0 , S₃ =1/2 this implies S=1/2

now S₁₂ =1 and S₃ =1/2 this implies S= (1/2-1).....(1/2+1) =   1/2, 3/2 (for baryons)