Consider the following statements (X and Y st | vedclass

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(C) For a nucleus,${ }_Z^A X$,the mass number is $A = N + Z$,where $N$ is the number of neutrons and $Z$ is the number of protons.$(I)$ In ${ }_{32}^{

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Only statements $II, III$ and $IV$ are correct

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(C) For a nucleus,${ }_Z^A X$,the mass number is $A = N + Z$,where $N$ is the number of neutrons and $Z$ is the number of protons.$(I)$ In ${ }_{32}^{65} X$ and ${ }_{33}^{65} Y$,the atomic numbers $(Z)$ are $32$ and $33$ respectively. Since $Z$ is different,they are not isotopes. This statement is incorrect.$(II)$ In ${ }_{42}^{86} X$ and ${ }_{42}^{85} Y$,the atomic numbers $(Z)$ are both $42$. Since they have the same $Z$ but different mass numbers $(A)$,they are isotopes. This statement is correct.$(III)$ For ${ }_{85}^{174} X$,$N = 174 - 85 = 89$. For ${ }_{88}^{177} Y$,$N = 177 - 88 = 89$. Since both have $89$ neutrons,this statement is correct.$(IV)$ In ${ }_{92}^{235} X$ and ${ }_{94}^{235} Y$,both have the same mass number $(A = 235)$. Nuclei with the same mass number are called isobars. This statement is correct.Therefore,statements $(II), (III),$ and $(IV)$ are correct.

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