Question

Determine the number of protons and the number of neutrons in each isotope. \begin{equation}\text { a. }^{14} \mathrm{N} \quad\quad\quad\quad\quad \text { b. }_{11}^{23} \mathrm{Na}\end{equation} \begin{equation}\quad\quad \text { c. }\frac{222 \mathrm{Rn}}{86} \mathrm{Rn} \quad\quad \text { d. } \quad \frac{208}{82} \mathrm{Pb}\end{equation}

Short answer

For Nitrogen-14: 7 protons, 7 neutrons. For Sodium-23: 11 protons, 12 neutrons. For Radon-222: 86 protons, 136 neutrons. For Lead-208: 82 protons, 126 neutrons.

Step-by-step solution

Identify Atomic Number and Mass Number for Nitrogen-14 (N-14)

For isotope abla14N, the lower number (7) is the atomic number, which is the number of protons. The upper number (14) is the mass number, which is the sum of protons and neutrons.

Calculate Neutrons for Nitrogen-14 (N-14)

Subtract the atomic number from the mass number to find the number of neutrons: 14 - 7 = 7 neutrons.

Identify Atomic Number and Mass Number for Sodium-23 (Na-23)

For isotope abla23Na, the lower number (11) is the atomic number indicating 11 protons, and the upper number (23) is the mass number.

Calculate Neutrons for Sodium-23 (Na-23)

Subtract the atomic number from the mass number to find the number of neutrons: 23 - 11 = 12 neutrons.

Identify Atomic Number and Mass Number for Radon-222 (Rn-222)

For isotope abla222Rn, the lower number (86) represents the atomic number indicating 86 protons, and the upper number (222) is the mass number.

Calculate Neutrons for Radon-222 (Rn-222)

Subtract the atomic number from the mass number to find the number of neutrons: 222 - 86 = 136 neutrons.

Identify Atomic Number and Mass Number for Lead-208 (Pb-208)

For isotope abla208Pb, the lower number (82) represents the atomic number, indicating 82 protons, and the upper number (208) is the mass number.

Calculate Neutrons for Lead-208 (Pb-208)

Subtract the atomic number from the mass number to find the number of neutrons: 208 - 82 = 126 neutrons.

Key concepts

Atomic Number

The atomic number of an element is fundamental in understanding chemistry and represents a unique identifier for each chemical element. In an element symbol, such as ¹⁴N or ₁₁²³Na, the atomic number is displayed as the lower number beneath the element's symbol, which for nitrogen (N) is 7 and for sodium (Na) is 11.

An atomic number denotes the number of protons in the nucleus of an atom. Since the number of protons determines an element's identity, no two elements can have the same atomic number. For example, nitrogen always has 7 protons, whereas sodium always has 11. Protons carry a positive charge, and because atoms are neutral, the atomic number also tells us the number of electrons in an uncharged atom.

Understanding atomic numbers is crucial for categorizing elements in the periodic table and predicting how atoms will interact with each other. When dealing with isotopes, the atomic number remains constant, while other characteristics, such as the number of neutrons, can vary.

Mass Number

The mass number is key to identifying different isotopes of the same element. This number is represented in the nuclear symbol at the upper left of the element's symbol. For instance, the mass number of nitrogen in ¹⁴N is 14, while for sodium in ₁₁²³Na, it is 23.

The mass number corresponds to the total number of protons and neutrons in the nucleus of an atom. It provides a rough estimate of the atom's mass. Every isotope of a given element has the same number of protons (its atomic number), but the number of neutrons can vary. This variance in neutron number is what creates isotopes. For instance, ¹²C and ¹⁴C are both isotopes of carbon, but ¹⁴C has two more neutrons in its nucleus.

In calculations, once you know the mass number and atomic number, you can quickly find the number of neutrons. For teaching purposes, it is critical to emphasize the distinct roles of the mass number and the atomic number when defining isotopes.

Number of Neutrons

Neutrons play a crucial role in the stability and identity of isotopes. Unlike protons, the number of neutrons in an atom's nucleus can vary even among atoms of the same element without changing its atomic number. It's this variability that gives rise to isotopes.

To calculate the number of neutrons in an isotope, one must simply subtract the atomic number from the mass number. Taking nitrogen-14 (¹⁴N) as an example, with an atomic number of 7 and a mass number of 14, we find that there are 7 neutrons (14 - 7 = 7). Similarly, sodium-23 (₁₁²³Na) with an atomic number of 11 has 12 neutrons (23 - 11 = 12).

The number of neutrons affects an isotope's mass and can influence the stability of an atom. Some isotopes with a high number of neutrons are unstable and subject to radioactive decay. Understanding the calculation of neutrons is pivotal for students to grasp the concept of isotopes and their different forms.