Question

The mass of a neutron is \(1.6749 \times 10^{-24} \mathrm{~g}\), and the mass of a proton is \(1.6726 \times 10^{-24} \mathrm{~g} .\) What is the total mass of a neutron and a proton?

Short answer

The total mass is \(3.3475 \times 10^{-24} \text{ g}\).

Step-by-step solution

Identify the Masses

The given masses are: the mass of a neutron is \(1.6749 \times 10^{-24} \text{ g}\) and the mass of a proton is \(1.6726 \times 10^{-24} \text{ g}\). These are the values we need to add.

Set Up the Addition

We need to add the two given masses to find the total mass. We can write this as:\[1.6749 \times 10^{-24} + 1.6726 \times 10^{-24}\]

Perform the Addition

Add the numbers normally: \(1.6749 + 1.6726 = 3.3475\).Since they are both in the same order of magnitude \(\times 10^{-24}\), we keep this factor in the result: \[3.3475 \times 10^{-24} \text{ g}\].

Key concepts

Neutron

Neutrons are fascinating subatomic particles that reside within the nucleus of an atom. They are neutral, thus lacking any electrical charge, which differentiates them from other nucleons like protons. The primary role of neutrons, along with protons, is to contribute to the atomic mass of an atom.
Neutrons were first discovered by James Chadwick in 1932, a breakthrough that advanced our understanding of atomic structure. They are slightly heavier than protons, as you can see from their mass of \(1.6749 \times 10^{-24} \text{ g}\). This slight difference makes neutrons essential for the stability of most atomic nuclei.
Without neutrons, protons would repel each other due to their positive charges. This makes neutrons critical in holding the nucleus together, a phenomenon facilitated by the strong nuclear force. Overall, neutrons play a significant role in the mass and stability of elements, influencing properties like isotopes.

Proton

Protons are positively charged particles found in the nucleus of an atom. They are counted to determine the atomic number of an element, which effectively defines the element itself. Each proton has a mass of \(1.6726 \times 10^{-24} \text{ g}\), just slightly lighter than neutrons.
Protons contribute fundamentally to the mass of an atom and, along with neutrons, compose the atomic nucleus. The number of protons within the nucleus determines the chemical properties and identity of the element. For instance, all atoms with one proton are hydrogen atoms.

• Protons possess a positive charge, denoted as \(+1\).
• This positive charge attracts negatively charged electrons, keeping them in orbit around the nucleus.

By binding together with neutrons through the strong nuclear force, protons help to provide stability to the atom. They also interact with other subatomic particles, participating in nuclear reactions such as fusion and fission.

Mass Addition

Mass addition is a straightforward arithmetic process, yet it plays a crucial role in understanding atomic mass. When adding the masses of subatomic particles like neutrons and protons, it is essential to keep track of their scale, given in scientific notation. In the given exercise, we added the masses of a neutron and a proton, which are already conveniently presented in the same magnitude. This makes the addition simpler. Here is how:1. **Write Down the Masses:** Start with the masses given: \(1.6749 \times 10^{-24} \text{ g}\) for the neutron and \(1.6726 \times 10^{-24} \text{ g}\) for the proton.2. **Add the Masses:** Simply add these numbers directly, as they share the same power of ten, ensuring no additional conversions are needed. Thus, \[1.6749 + 1.6726 = 3.3475 \].3. **Retain the Exponent:** Retain the \(\times 10^{-24}\), because the base numbers added do not change the exponent in scientific notation.This results in a total mass of \(3.3475 \times 10^{-24} \text{ g}\), representing the combined mass of a neutron and a proton. Mass addition allows for calculating the mass of entire atoms and molecules, crucial in fields like chemistry and physics where precise measurements are necessary.