Problem 1 - College Physics

Question

How many protons and how many neutrons are there in a nucleus of (a) neon, \(_{10}^{21} \mathrm{Ne}(\mathrm{b})\) zinc, \(_{30}^{65} \mathrm{Zn}(\mathrm{c})\) silver, \(_{47}^{108} \mathrm{Ag}\)

Step-by-Step Solution

Answer

Neon: 10 protons, 11 neutrons; Zinc: 30 protons, 35 neutrons; Silver: 47 protons, 61 neutrons.

Step 1: Understanding Notation

Each notation, such as \(_{10}^{21} \, \mathrm{Ne}\), represents the element with its atomic number (subscript) and mass number (superscript). The atomic number represents the number of protons, and the mass number is the sum of protons and neutrons in the nucleus.

Step 2: Determining Protons in Neon

For \(_{10}^{21} \, \mathrm{Ne}\), the atomic number is 10, meaning there are 10 protons in a neon nucleus.

Step 3: Determining Neutrons in Neon

For \(_{10}^{21} \, \mathrm{Ne}\), subtract the atomic number (10) from the mass number (21). This gives 21 - 10 = 11 neutrons.

Step 4: Determining Protons in Zinc

For \(_{30}^{65} \, \mathrm{Zn}\), the atomic number is 30, meaning there are 30 protons in a zinc nucleus.

Step 5: Determining Neutrons in Zinc

For \(_{30}^{65} \, \mathrm{Zn}\), subtract the atomic number (30) from the mass number (65). This gives 65 - 30 = 35 neutrons.

Step 6: Determining Protons in Silver

For \(_{47}^{108} \, \mathrm{Ag}\), the atomic number is 47, meaning there are 47 protons in a silver nucleus.

Step 7: Determining Neutrons in Silver

For \(_{47}^{108} \, \mathrm{Ag}\), subtract the atomic number (47) from the mass number (108). This gives 108 - 47 = 61 neutrons.

Key Concepts

Atomic Number

The atomic number is a fundamental property of an element.It is represented by the subscript in the nuclear notation of an element, such as the 10 in \(_{10}^{21} \, \mathrm{Ne}\).This number reveals the identity of the element by specifying the number of protons found in the nucleus.In a neutral atom, it also indicates the number of electrons surrounding the nucleus because protons and electrons are equal.

• Atomic number specifies the element.
• It equals the number of protons.
• It helps identify the element and its properties.

The atomic number is the same for all atoms of an element, regardless of the isotope.This is why elements are ordered by their atomic numbers in the periodic table.

Mass Number

The mass number of an element distinguishes isotopes of the same element.It is indicated by the superscript in the nuclear symbol, like the 21 in \(_{10}^{21} \, \mathrm{Ne}\).Mass number is the sum of the protons and neutrons in the nucleus, which account for nearly all of the atomic mass.

• Mass number = number of protons + number of neutrons.
• The mass number varies among isotopes of the same element.

The mass number is crucial because it affects the stability and radioactivity of an isotope.While it doesn't appear in the periodic table, it is vital for understanding isotopic variations.

Protons

Protons are positively charged particles that reside in the atomic nucleus.They are a key component of the atomic structure, defining what element an atom is.Protons bear a charge of +1 and have a relative mass similar to that of neutrons.

• Number of protons = atomic number.
• Protons contribute to the overall positive charge of the nucleus.
• They collaborate with neutrons to stabilize the nucleus.

Observing \(_{10}^{21} \, \mathrm{Ne}\), we see there are 10 protons, marking it as neon.Variations in the number of protons change the element entirely, as it alters the atomic number.

Neutrons

Neutrons are neutral particles that reside within the atomic nucleus alongside protons.They do not carry any charge, but they contribute significantly to the mass of the atom.Neutrons play a crucial role in stabilizing the nucleus, particularly in heavier elements where their numbers increase.

• Neutrons = mass number - atomic number.
• They provide nuclear stability.
• They vary in number among different isotopes of the same element.

For example, the isotope \(_{30}^{65} \, \mathrm{Zn}\) has 35 neutrons, calculated by subtracting the atomic number 30 from the mass number 65.Understanding neutrons also helps grasp concepts like isotopic differences and nuclear reactions.