The atomic number is the number of protons present in the nucleus of an atom. This number does not change without changing the element. In elemental notation, the atomic number is found at the bottom left corner of the chemical symbol for the element. The upper number represents the nuclear mass of the atom, given by the sum of the protons and neutrons.

Elemental notation gives us insight into the particles that are found in a given atom. The atomic number in the lower left corner shows how many protons are in an atom, and the mass number in the upper left corner shows how many protons and neutrons are in an atom. As a result, we can find the number of neutrons in the ion in question by subtracting the atomic number from the mass number:

There are twenty neutrons in this potassium ion.

Let's start by identifying our starting atom. Cobalt has 27 protons. If the given atom has an atomic mass of 60, then it must have 33 neutrons.

An alpha decay is the emission of a helium nucleus with mass 4 (2 protons and 2 neutrons). This results in a daughter nuclide whose atomic number is 2 less and atomic mass is 4 less than the original element.

A beta decay is the conversion of a neutron to a proton, accompanied by the emission of an electron. This results in a daughter nuclide whose atomic number is 1 more than the original element, with no change to atomic mass. This process is done twice.

Doing 1 alpha and 2 beta decays gives a net change of -4 for the atomic mass and 0 for the atomic number.

To do this problem, all you have to remember is that the sum of the atomic numbers and atomic masses should be equal on the left and right sides.

Mass values: 

Atomic numbers: 

Look at your periodic table to find the identity of the resulting element.

The resulting element has the same atomic mass and the atomic number has increased by 1. This means that a neutron has been converted into a proton, and an electron has been emmitted; this happens in beta decay.

Beta decay:

 This is the standard isotopic notation.  is the mass number which is equal to the number of protons plus neutrons, and  is equal to the atomic number. Thus,  is a sodium atom with 12 neutrons.

 This is the standard isotopic notation.  is the mass number which is equal to the number of protons plus neutrons, and  is equal to the atomic number. Sometimes, the atomic number is left out since it can be easily found using the atomic symbol and the periodic table. Thus,  is a carbon atom (all of which have 6 protons) with 8 neutrons, giving us a mass number of 14.

Isotopes of elements have different numbers of neutrons, and different atomic weights, but must have the same number of protons. For example, carbon exists as isotopes of C12, C13, and C14, but these are all carbon atoms and have exactly 6 protons. The number of neutrons, and thus atomic weight varies between isotopes. Also, different isotopes may have different chemical properties, such as half-life and type of radioactive decay.

The element is either found by looking at the symbol "C" and identifying it on the periodic table as carbon, or by looking at the atomic number. The isotopic notation given is in the form of

Where X is the symbol for the element, Z is the atomic number (number of protons) and A is the atomic mass number (number of protons plus number of neutrons).

Since the atomic number is 6 we can also find this on the periodic table to be carbon. The isotope now can be written as 

To find the number of neutrons we take 

Radioactive decay is the result of an unstable nucleus in an atom. When an atom contains more neutrons than the nucleus can handle it will undergo radioactive decay, leading to emission of different particles such as alpha particles or beta electrons. This can occur in ground state elemental atoms, but is most commonly seen in radioactive isotopes. Isotopes contain the same number of protons as any other atom of a given element, but often contain a greater number of neutrons, leading to instability. These neutrons will be lost via radioactive decay in order for the atom to reach the ground state, the most stable isotope.

Ionization results in a charged particle via electron transfer, but does not contribute to radioactivity.