Question

how many protons, neutrons, and electrons are in this ion?
75 as^{3+}
33
75 p^{+}, 33 n^{0}, 33 e^{-}
33 p^{+}, 42 n^{0}, 33 e^{-}
33 p^{+}, 75 n^{0}, 33 e^{-}
33 p^{+}, 42 n^{0}, 30 e^{-}

Explanation:

Step1: Determine the number of protons

The atomic number \(Z\) (subscript) gives the number of protons. For \(_{33}^{75}\text{As}^{3 +}\), \(Z = 33\), so the number of protons \(p^{+}=33\).

Step2: Calculate the number of neutrons

The mass number \(A\) (superscript) is related to the atomic number \(Z\) by \(A=Z + N\), where \(N\) is the number of neutrons. Given \(A = 75\) and \(Z = 33\), then \(N=A - Z=75 - 33 = 42\).

Step3: Find the number of electrons

For a neutral atom, the number of electrons \(e^{-}\) equals the number of protons. But for a cation \(\text{As}^{3+}\), the number of electrons is less than the number of protons. The charge \(q = + 3\), and \(q=p^{+}-e^{-}\). So \(e^{-}=p^{+}-q=33 - 3=30\).

Answer:

\(33\ p^{+},42\ n^{0},30\ e^{-}\) (corresponding to the last option \(33\ p^{+},42\ n^{0},30\ e^{-}\))