How many neutrons are produced when plutonium-239 is bombarded with an $\alpha$ particle to form americium-240 and a proton?

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When plutonium-239 is bombarded with an alpha particle (which has 2 protons and 2 neutrons), it forms americium-240 and a proton. The equation for this reaction is: $$ \text{Pu}^{239} + \alpha \rightarrow \text{Am}^{240} + \text{p}^+ $$ To conserve the number of nucleons (protons + neutrons), the number of neutrons produced must be 2, because the alpha particle adds 4 nucleons to plutonium-239 (making a total of 243 nucleons), but the resulting americium-240 and a proton account for 241 nucleons, leaving 2 neutrons unaccounted for, which are thus produced in the reaction.

How Many Neutrons Are Produced When Plutonium-239 Is Bombarded with An \alpha