A particle and antiparticle pair annihilate converting their mass to pure energy (eg- electron positron annihilation) if they both have different spins their spin before and after annihilation is zero but if they have same spins can they annihilate? because if they do wouldn't that violate conservation of spin?
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In $e^+ e^+ \to \gamma \gamma$, the total angular momentum in the initial state (i.e. $e^+ e^-$) and the one in the final state (i.e. $\gamma \gamma$) are the same. This applies to any process in particle physics as the total angular momentum is a conserved quantity.
It is unclear what you mean by "particle and antiparticle convert their mass into pure energy". Like angular momentum, also energy (and momentum) are conserved quantities. Denoting the momenta of $e^\pm$ by $\vec{p}_{1,2}$ and the momenta of the photons by $\vec{q}_{1,2}$, energy-momentum conservation in $e^+ e^- \to \gamma \gamma$ is expressed by the equations $$ c\sqrt{m_e^2c^2+ \vec{p}_1^2}+ c\sqrt{m_e^2c^2+\vec{p}_2^2}= c|\vec{q}_1|+ c|\vec{q}_2|, \qquad \vec{p}_1+\vec{p}_2=\vec{q}_1+\vec{q}_2.$$ Note that the relativistic energy-momentum relation reads $E=c \sqrt{m^2 c^2+ \vec{p}^2}$. In the case of a photon, where $m_\gamma=0$, the energy-momentum relation is thus given by $E_\gamma= c |\vec{p}_\gamma|$.
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