Question

Give the number of protons, neutrons, and electrons in the following isotopes: (a) \(\mathrm{Al}-27\) (b) \({ }_{14}^{28} \mathrm{Si}\) (c) \(\mathrm{B}-11\) (d) \({ }_{47}^{115} \mathrm{Ag}\)

Short answer

(a) Al-27: 13p, 14n, 13e. (b) Si-28: 14p, 14n, 14e. (c) B-11: 5p, 6n, 5e. (d) Ag-115: 47p, 68n, 47e.

Step-by-step solution

Identify Atomic Numbers and Mass Numbers

For each isotope, identify the atomic number (Z) and the mass number (A). The atomic number is the number of protons and electrons in a neutral atom, and the mass number is the sum of protons and neutrons. For example, in Al-27, Z = 13 (from periodic table) and A = 27.

Calculate Number of Protons

Since the atomic number (Z) is equal to the number of protons, use the atomic number to determine the number of protons for each isotope. For example, for \( \text{Al-27} \), Z = 13, so protons = 13.

Determine Number of Electrons

In a neutral atom, the number of electrons is equal to the number of protons. Therefore, for \( \text{Al-27} \), electrons = 13.

Find Neutrons Using Mass Number

Calculate the number of neutrons by subtracting the atomic number from the mass number: neutrons = A - Z. For \( \text{Al-27} \), neutrons = 27 - 13 = 14.

Calculate for \( \text{Si-28} \)

Given \({ }_{14}^{28} \text{Si}\), Z = 14, A = 28. Protons = 14, Electrons = 14, Neutrons = 28 - 14 = 14.

Calculate for \( \text{B-11} \)

For \( \text{B-11} \), Z = 5. Thus, protons = 5, electrons = 5, and neutrons = 11 - 5 = 6.

Calculate for \( \text{Ag-115} \)

Given \({ }_{47}^{115} \text{Ag}\), Z = 47, A = 115. Protons = 47, Electrons = 47, Neutrons = 115 - 47 = 68.

Compile the Results

Summarize the findings: (a) Al-27 has 13 protons, 14 neutrons, 13 electrons. (b) Si-28 has 14 protons, 14 neutrons, 14 electrons. (c) B-11 has 5 protons, 6 neutrons, 5 electrons. (d) Ag-115 has 47 protons, 68 neutrons, 47 electrons.

Key concepts

Protons and Neutrons

Protons and neutrons are the building blocks of an atom's nucleus. Each element on the periodic table features a specific number of protons. This distinguishes one element from another. Protons carry a positive charge, which contributes to the overall electrical charge balance in an atom.
Neutrons, on the other hand, have no electrical charge. They add to the mass of the atom, and together with protons, they define the isotope of an element. Neutrons play a crucial role in the stability of the nucleus by offsetting electrostatic repulsion between protons.

• Protons determine the element's identity.
• Neutrons contribute to the isotope's characteristics and atomic stability.

Understanding protons and neutrons helps in solving exercises involving atomic calculations.

Isotopes

Isotopes are variations of elements that contain the same number of protons but a different number of neutrons. This means isotopes have the same atomic number but different mass numbers. For example, in the isotope \( \text{Al-27} \), both 'Al-27' and 'Al-25' would be isotopes of aluminum, where the 27 and 25 represent the mass numbers.
This variation in neutron count affects the mass, but not the chemical properties of the element. Thus, isotopes can behave identically in chemical reactions.

• All isotopes of an element have identical chemical properties.
• Isotopes can have different physical properties due to variations in mass.

Learning about isotopes is essential for understanding nuclear chemistry and atomic structure.

Atomic Number

The atomic number is a fundamental property of an element. It is equal to the number of protons found in the nucleus of an atom. Since atoms are neutral, the number of protons is also equal to the number of electrons in a neutral atom. Thus, the atomic number gives you a clear count of both protons and electrons.
For example, in the exercise, Si (silicon) has an atomic number of 14, indicating 14 protons and 14 electrons. Knowing the atomic number helps in predicting chemical behavior and categorizing elements in the periodic table.

• Atomic number defines the element's position on the periodic table.
• Atomic number equals the proton count, governing electron arrangements.

Understanding the atomic number is key to mastering basic chemistry concepts.

Mass Number

Mass number is the total count of protons and neutrons in an atom's nucleus. It is represented as 'A' in nuclear notation, such as \( { }_{Z}^{A} \) where Z is the atomic number. Mass number is used to differentiate between isotopes of an element.
For example, the element \( \text{Ag-115} \) has a mass number of 115. This means the sum of protons and neutrons equals 115. You can calculate the number of neutrons by subtracting the atomic number from the mass number.

• Mass number = Protons + Neutrons.
• Identifies different isotopes of the same element.

The mass number plays a crucial role in understanding the composition of atoms and calculating atomic weights.