Problem 53 - Chemistry A Molecular Approach

Question

Determine the number of protons and the number of neutrons in each isotope. a. \({ }_{7}^{14} \mathrm{~N}\) b. \(\frac{23}{11} \mathrm{Na}\) c. \(\frac{222}{86} \mathrm{Rn}\) d. \(\frac{208}{82} \mathrm{Pb}\)

Step-by-Step Solution

Answer

a. Nitrogen: 7 protons, 7 neutrons; b. Sodium: 11 protons, 12 neutrons; c. Radon: 86 protons, 136 neutrons; d. Lead: 82 protons, 126 neutrons.

Step 1: Understanding Atomic Number and Mass Number

The lower number in isotopic notation represents the atomic number (Z), which is the number of protons in the nucleus of the atom. The upper number is the mass number (A), which is the sum of the number of protons and the number of neutrons.

Step 2: Calculating the Number of Protons for Each Isotope

For each isotope, the number of protons is equal to the atomic number (Z). For (a) Nitrogen has 7 protons as the atomic number is 7; (b) Sodium has 11 protons since the atomic number is 11; (c) Radon has 86 protons as the atomic number is 86; (d) Lead has 82 protons because the atomic number is 82.

Step 3: Calculating the Number of Neutrons for Each Isotope

The number of neutrons in an isotope can be determined by subtracting the atomic number (Z) from the mass number (A). For (a) Nitrogen has 7 neutrons (14 - 7); (b) Sodium has 12 neutrons (23 - 11); (c) Radon has 136 neutrons (222 - 86); (d) Lead has 126 neutrons (208 - 82).

Key Concepts

Atomic Number

The atomic number is a fundamental property of an element and it tells us the number of protons in the nucleus of an atom. Protons are positively charged particles, and the atomic number uniquely identifies the chemical element. In other words, no two different elements can have the same atomic number. For instance, the atomic number of hydrogen is 1, meaning every atom of hydrogen has exactly one proton in its nucleus.

It is symbolized by the letter Z and is always an integer. When looking at the periodic table, elements are arranged in order of increasing atomic number. Knowing the atomic number allows you to determine the identity of an element and its position in the periodic table. It also informs you about the number of electrons in a neutral atom, which equals the number of protons due to the balance of charges.

Mass Number

The mass number, symbolized by A, is the total number of protons and neutrons in an atom's nucleus. It's important to remember that the mass number is not the same as the atomic mass - the latter is a weighted average of all the isotopes of an element and is not necessarily a whole number.

Neutrons and protons contribute nearly equally to the atomic mass, given that they are close in mass with neutrons being slightly heavier. Electrons, on the other hand, are so light in comparison that they do not significantly contribute to the mass number. To calculate the number of neutrons in an atom, you subtract the atomic number from the mass number: \[ \text{Number of neutrons} = A - Z \]
For example, if an atom has a mass number of 23 and an atomic number of 11, it would have 23 - 11 = 12 neutrons.

Protons and Neutrons

Protons and neutrons are the particles that make up the nucleus of an atom. Protons have a positive charge, while neutrons have no charge - they are neutral. The number of protons in the nucleus defines the element, while the number of neutrons can vary within atoms of the same element, creating different isotopes.

Isotopes are atoms with the same atomic number but different mass numbers due to a different number of neutrons. The properties of isotopes of an element are mostly similar, but they can have different nuclear stabilities and mass, which influences their behavior in certain processes, such as nuclear reactions or decay. The binding energy, or the energy that holds the nucleus together, is also affected by the neutron-proton ratio.

Isotopic Notation

Isotopic notation is a way to represent isotopes symbolically. It includes the element symbol, the mass number at the upper left, and the atomic number at the lower left. The general form can be expressed as:\[\,_{Z}^{A}\text{X}\]where X is the chemical symbol of the element, A is the mass number, and Z is the atomic number. This notation provides quick and essential information about an isotope at a glance.For example, \(\,_{7}^{14}\text{N}\) indicates a nitrogen isotope with 7 protons (hence it's nitrogen as its atomic number is 7) and a mass number of 14, which means it has 7 neutrons (14 - 7). Isotopic notation is particularly useful when discussing nuclear reactions and the behavior of isotopes in various scientific and medical applications.