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Isotopes have same atomic number. They have different mass numbers. Their physical properties are different.
atomic charge
Stability depends on to proton/neutron ratio; and this ratio increase with the atomic number.
The band of stability contain stable isotopes.
to get stability
The stability of a nucleus depends on the ratio of protons to neutrons. It's not a simple ratio that's the same for all atomic numbers, it varies. For small atomic numbers, 1:1 is about right. For higher atomic numbers, more neutrons are needed.
The atomic number the the number of protons and therefore the total positive charge in the nucleus. So the the element with the atomic number 82 has more protons and a greater nuclear charge then the atomic number of 81. More protons can mean many different things such as a smaller radius, greater first ionisation energy or greater electronegativity.
The neutron is the particle in the atomic nucleus that carries no charge.
Neutrons and protons both are located at the atomic nucleus. Protons carry +1 charge each. Neutrons carry no charge.
If an element is radioactive, it refers to the stability of their atomic nucleus. If that atomic nucleus is not stable, it is considered radioactive.
It may or may not equal, neutrons are responsible for stability of nucleus.
A neutron is neutral, meaning no charge.