When two elements have the same atomic number but different mass numbers within their respective periods of the periodic table, it means they are isotopes of the same element. Isotopes are atoms of the same element that have different numbers of neutrons in their nuclei, resulting in different mass numbers.
In the periodic table, elements are arranged in periods (horizontal rows) based on their atomic number, which corresponds to the number of protons in the nucleus. Within a period, elements have the same number of electron shells.
However, different isotopes of an element have varying numbers of neutrons, which affects their mass numbers. The mass number is the sum of the protons and neutrons in an atom's nucleus. Isotopes of an element have the same number of protons (atomic number) since they belong to the same element, but they differ in the number of neutrons.
For example, let's consider hydrogen. Hydrogen has three isotopes: hydrogen-1 (mass number 1), deuterium (hydrogen-2, mass number 2), and tritium (hydrogen-3, mass number 3). They all have one proton in their nuclei (atomic number 1) but differ in the number of neutrons.
Similarly, carbon-12 (mass number 12) and carbon-14 (mass number 14) are isotopes of carbon. They both have six protons (atomic number 6) but differ in the number of neutrons.
The presence of different isotopes of an element does not change its chemical properties significantly since isotopes have the same number of protons and electrons, and it is primarily the arrangement of electrons that determines chemical behavior. However, isotopes can have different physical properties, such as varying atomic masses and stabilities, which can be useful in various scientific and practical applications.