You can determine the number of protons and electrons without difficulty, but you can never determine the number of neutrons based on the information provided. There are four stable isotopes of calcium. The most abundant is calcium-40. All isotopes of the same element have the same number of protons, but different numbers of neutrons. In order to determine the number of neutrons, you must specify the isotope by giving its mass number.
The ionic charge tells the number of electrons gained or lost. Since electrons are negative, adding an electron will make the ion have a negative charge, and losing electrons will make for a positively charged ion.
A calcium(II) ion, Ca2+, has 20 protons and 18 electrons because it has lost two (to give it the +2 charge). Again, it's impossible to say how many neutrons.
Chloride ion has gained 1 electron, and therefore, has 17 protons and 18 electrons, and again, it's impossible to say how many neutrons without specifying the mass number of the chlorine isotope.
Finally, you've specified an actual isotope. Calcium-41 has 20 protons, 20 electrons and 21 neutrons. The mass number, 41, is the sum of the protons and neutrons.
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The Skipper says, "Neutrons = atomic weight - atomic number = 40-20 = 20 neutrons." This is what Gilligan might say, and it's wrong. You can't determine the number of neutrons unless you know the mass number for the particular isotope. The "atomic weight" is NOT the mass number.
And this is even worse: "Cl neutrons = 35.453 - 17 = 18.453. Can't have a non-integer number of neutrons so Cl must be a mixture of isotopes."
Of course its a mixture of isotopes. That is where the 35.453 amu comes from. It is the WEIGHTED AVERAGE of all of the naturally occurring isotopes of chlorine. 35.453 amu is NOT the number of protons and neutrons. The mass number is the number of protons + neutrons and it is a whole number, a counting number, an integer because it COUNTS the number of particles in the nucleus.142