Indicate the number of protons and neutrons in the following nuclei: $(\mathbf{a}){ }^{239} \mathrm{Pu},(\mathbf{b}){ }^{142} \mathrm{Ba},(\mathbf{c})\( potassium- \)41 .$.

First, let's find the atomic numbers of the given elements from the periodic table: a) Pu (Plutonium) has an atomic number (Z) of 94. b) Ba (Barium) has an atomic number (Z) of 56. c) K (Potassium) has an atomic number (Z) of 19.

Now that we have the atomic numbers, the number of protons is equal to the atomic number (Z). Calculate the number of neutrons by subtracting the atomic number (Z) from the atomic mass number (A). a) For Pu: Number of protons = Atomic Number (Z) = 94 Number of neutrons = Atomic Mass Number (A) - Atomic Number (Z) = 239 - 94 = 145 b) For Ba: Number of protons = Atomic Number (Z) = 56 Number of neutrons = Atomic Mass Number (A) - Atomic Number (Z) = 142 - 56 = 86 c) For Potassium-41: Number of protons = Atomic Number (Z) = 19 Number of neutrons = Atomic Mass Number (A) - Atomic Number (Z) = 41 - 19 = 22 The number of protons and neutrons in each isotope is as follows: a) \(^{239}\mathrm{Pu}\): 94 protons and 145 neutrons. b) \(^{142}\mathrm{Ba}\): 56 protons and 86 neutrons. c) Potassium-41: 19 protons and 22 neutrons.