Problem 116 Why is it impossible for an elem... [FREE SOLUTION]

Chapter 2: Problem 116

Why is it impossible for an element to have a mass number less than its atomic number?

Short Answer

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The atomic number of an atom denotes the number of protons, while the mass number represents the total number of protons and neutrons. Since the mass number is equal to the atomic number plus the number of neutrons, and neither protons nor neutrons can be in negative quantities, it is impossible for the mass number to be less than the atomic number. Therefore, no element can have a mass number less than its atomic number.

Step by step solution

Understanding Atomic Number and Mass Number

The atomic number of an atom is the number of protons it possesses which is unique to each element, while the mass number is the total number of protons and neutrons in an atom's nucleus. Neutrons and protons are both nucleons, which are located in the atomic core, and are thus part of the mass number. Electrons are not included in the mass number because their mass is significantly smaller and can be disregarded when compared to the mass of protons and neutrons.

Identifying the Relationship Between Atomic and Mass number

Every atom has at least one proton (since the atomic number equals the number of protons and there's no element with an atomic number of zero) and could possibly have neutrons as well (included in the mass number). This means that the mass number, being the total number of protons and neutrons, must be equal to or larger than the atomic number (the number of protons only).

Conclusion

Given that the atomic number denotes number of protons and mass number denotes total number of protons and neutrons, it is impossible for an element to have a mass number less than its atomic number. This is due to the fact that mass number includes the atomic number (protons) and additional neutrons, none of which can be in negative quantities. In other words, the mass number will always be a value equal to or greater than the atomic number.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mass Number

The mass number is a concept central to understanding the identity and structure of an atom. It is the sum of all protons and neutrons present within the nucleus of an atom. These particles, known as nucleons, contribute significantly to the atom's mass.
As electrons have negligible mass and do not reside in the nucleus, they are excluded when calculating the mass number.
To demonstrate:

If an atom has 6 protons and 6 neutrons, its mass number is 12.
The formula to calculate mass number is: \( A = Z + N \), where \( A \) is the mass number, \( Z \) represents the number of protons, and \( N \) is the number of neutrons.

Remember, the mass number is critical because it helps to distinguish between different isotopes of the same element, which have the same number of protons but different numbers of neutrons.

Protons

Protons are subatomic particles found in the nucleus of an atom and carry a positive charge. The number of protons in an atom is known as the atomic number, represented by the symbol \( Z \). It defines the chemical element to which the atom belongs.
For example, all carbon atoms have an atomic number of 6, indicating 6 protons.

This atomic number is unique to each element, meaning no two different elements will have the same number of protons.
Protons, alongside neutrons, add to the atomic mass, though they do not define the mass number alone.
Without protons, an atom would not be considered a part of any element, as they form the identity of an element.

Protons play a vital role not only in identifying the element, but also in determining the atom's chemical properties and its place in the periodic table.

Neutrons

Neutrons are neutral particles found in the nucleus of an atom. They do not carry any electric charge, hence their name. Despite not affecting the electric charge of an atom, neutrons significantly influence the mass and stability of an atom.
Their quantity, together with protons, makes up the mass number.

Unlike protons, neutrons can vary within the same element, giving rise to different isotopes.
The presence of different neutron numbers accounts for variations in mass number among isotopes.
Isotopes have the same atomic number but differ in mass number due to varying neutron count.

Understanding neutrons is crucial when studying nuclear reactions and radioactivity, as these processes often involve changes in the number of neutrons within nuclei.

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Why is it impossible for an element to have a mass number less than its atomic number?

Short Answer

Step by step solution

Understanding Atomic Number and Mass Number

Identifying the Relationship Between Atomic and Mass number

Conclusion

Key Concepts

Mass Number

Protons

Neutrons

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