Question

\({ }_{14}^{30} \mathrm{Si},{ }_{15}^{31} \mathbf{p}\) and \({ }_{16}^{32} \mathrm{~S}^{a r e}\) (a) isotopes (b) isobars (c) isotones (d) none of these

Short answer

The atomic structures \({ }_{14}^{30} \mathrm{Si},{ }_{15}^{31} \mathrm{P}\) and \( { }_{16}^{32} \mathrm{S}\) are isotones, having the same number of neutrons.

Step-by-step solution

Identify each atom's atomic number and mass number

The subscript (lower number) is the atomic number (Z), which is the number of protons. The superscript (upper number) is the mass number (A), which is the number of protons plus neutrons. Let's determine them for each atom. For \({ }_{14}^{30} \mathrm{Si}\), Z=14 and A=30; for \({ }_{15}^{31} \mathrm{P}\), Z=15 and A=31; for \({ }_{16}^{32} \mathrm{S}\), Z=16 and A=32. So, the number of neutrons (N) is A-Z. Therefore, for \({ }_{14}^{30} \mathrm{Si}\), N=30-14=16; for \({ }_{15}^{31} \mathrm{P}\), N=31-15=16; and for \({ }_{16}^{32} \mathrm{S}\), N=32-16=16.

Classify the atoms

As they do not have the same atomic nor mass numbers, they cannot be classified as isotopes nor isobars. However, they all have the same neutron number (16), so they can be classified as isotones.

Key concepts

Atomic Number

The atomic number, often represented by the symbol \(Z\), is a fundamental property of an element. It is defined as the number of protons present in the nucleus of an atom. Since protons are positively charged, the atomic number also determines the element's identity and its position on the periodic table.
To find the atomic number of an element, you can look at the subscript in a nuclear notation. For example:

• In \({ }_{14}^{30} \mathrm{Si}\), the atomic number is 14.
• In \({ }_{15}^{31} \mathrm{P}\), the atomic number is 15.
• In \({ }_{16}^{32} \mathrm{S}\), the atomic number is 16.

Each change in atomic number represents a change to a different element.
This is because the number of protons strongly dictates the chemical properties and identity of the element.

Mass Number

The mass number, symbolized as \(A\), denotes the total number of protons and neutrons combined within the nucleus of an atom.
Although electrons are also present in an atom, they have negligible mass and do not contribute to the mass number.
Mass number can be identified by the superscript in the nuclear notation:

• For \({ }_{14}^{30} \mathrm{Si}\), the mass number is 30.
• For \({ }_{15}^{31} \mathrm{P}\), the mass number is 31.
• For \({ }_{16}^{32} \mathrm{S}\), the mass number is 32.

It is important to remember that the mass number is not the same as the atomic mass, which takes into account isotopic distribution and abundance.

Neutrons

Neutrons are uncharged particles found in the nucleus of an atom. They are crucial for the stability of the nucleus and play a significant role in the isotopic relationship between atoms.
To find the number of neutrons \(N\), you subtract the atomic number \(Z\) from the mass number \(A\):

• For \({ }_{14}^{30} \mathrm{Si}\), the number of neutrons is \(30 - 14 = 16\).
• For \({ }_{15}^{31} \mathrm{P}\), the number of neutrons is \(31 - 15 = 16\).
• For \({ }_{16}^{32} \mathrm{S}\), the number of neutrons is \(32 - 16 = 16\).

Atoms with the same number of neutrons, but different numbers of protons, are known as isotones.
In the given exercise, since all these atoms have 16 neutrons, they are classified as isotones.