Problem 55 - Physics for Scientists and Engineers with Modern Physics

Question

How many fundamental fermions are there in a water molecule?

Step-by-Step Solution

Answer

There are 64 fundamental fermions in a water molecule.

Step 1: Understand the composition of a water molecule

A water molecule (H₂O) consists of two hydrogen atoms and one oxygen atom. To find the number of fundamental fermions, we need to consider the subatomic particles in these atoms.

Step 2: Identify the fundamental fermions in hydrogen

Each hydrogen atom has one proton, which is composed of quarks, and one electron. The fundamental fermions in a hydrogen atom are one electron and the quarks making up the proton.

Step 3: Calculate fermions in the hydrogen atoms

Since a proton is made up of three quarks (two 'up' quarks and one 'down' quark), for two hydrogen atoms, we have two electrons and six quarks.

Step 4: Identify the fundamental fermions in oxygen

An oxygen atom has 8 protons, 8 neutrons, and 8 electrons. Each proton and neutron is made of 3 quarks. Therefore, in an oxygen atom, there are 8 electrons, and for the protons and neutrons combined, we have 48 quarks (16 particles * 3 quarks each).

Step 5: Combine the counts for the water molecule

Summing all the fermions in H₂O, we have the following: electrons (2 from hydrogen + 8 from oxygen) = 10, and quarks (6 from hydrogen + 48 from oxygen) = 54. Thus, the total number of fundamental fermions is 64.

Key Concepts

Water Molecule

A water molecule, represented by the chemical formula H₂O, is made of two hydrogen atoms and one oxygen atom. This simple structure is essential for life as we know it. Each part of this molecule is made up of smaller subatomic particles. Hydrogen contributes two atoms, and oxygen adds one in this molecule. Together, these atoms interact to form the properties that give water its unique characteristics, like being a liquid at room temperature, ability to dissolve many substances, and its high surface tension. Water molecule is a classic example of how simple combinations of atoms can result in complex behaviors crucial for biological functions.

Quarks

Quarks are fundamental constituents of matter. They combine in groups to form protons and neutrons—the particles that sit at the core of an atom. There are six types of quarks, but for our purposes, the 'up' and 'down' quarks are most important.

• Protons are made of two 'up' quarks and one 'down' quark.
• Neutrons are composed of two 'down' quarks and one 'up' quark.

These quark combinations contribute to the mass and charge of protons and neutrons, making them central to understanding atomic structure. In a water molecule, quarks are part of the protons and neutrons found in hydrogen and oxygen atoms.

Subatomic Particles

Subatomic particles include protons, neutrons, and electrons, which make up the atoms of a molecule. These components govern an atom's characteristics such as its mass, charge, and interactions with other atoms.

• Protons and neutrons: Found in the atomic nucleus and composed of quarks.
• Electrons: Negative charge carriers orbiting the nucleus.

Each subatomic particle plays a crucial role in defining the chemical properties of materials. In water, these subatomic particles determine how molecules bond and interact, influencing everything from its boiling point to its ability to act as a solvent.

Electrons

Electrons are tiny particles with a negative electrical charge, orbiting an atom's nucleus. Their distribution around the nucleus defines the types of chemical bonds and reactions an atom can participate in. Each hydrogen atom in H₂O contributes one electron, and the oxygen atom contributes eight, making up a total of ten electrons in a water molecule.

• Electrons are key in forming chemical bonds, especially covalent bonds like those in water.
• They are responsible for creating the energy levels within an atom.

The way electrons interact with each other is fundamental in creating the variety of chemical reactions and compounds necessary for diverse biological processes.