this question can be easily solved by balancing the mass number and atomic number of reactants and products of this reaction,
here reactants are Pu and a neutron and products: unknown element,Sr, 3 neutrons
total mass number of reactants= 239+1 =240 (a nuetron has mass number of 1)
let mass number of unknown element be x
total mass number of products=x+91+(3*1)=x+94
we know that ;total mass number of reactants=total mass number of products
so x+94=240; implies x=240-94=146 ;so mass number of unknown element =146
let atomic number of unknown element be y
total proton number of products=y+38+(3*0)=y+38
total proton number of reactants=94+0=94
total proton number of products=total proton number of reactants
so y+38=94 ; y=94-38=56 atomic number of unknown element is 56
now looking at options
146Ba56 matches our findings
so 146Ba56 is the answer
this problem is done based on conservation of mass.
thank you
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