Quick Answer
There are approximately 4.062 x 10^24 electrons in 0.990 oz of pure gold. This is calculated by first finding the number of gold atoms in 0.990 oz, then multiplying by the 79 electrons in each gold atom.
Calculating the Number of Gold Atoms
To find the number of electrons, we first need to calculate the number of gold atoms in 0.990 oz of pure gold. Here are the steps:
- The atomic mass of gold is 196.967 amu (atomic mass units)
- 1 oz equals 28.3495 grams
- 0.990 oz equals 28.046055 grams (0.990 * 28.3495)
- Use the formula: Number of Atoms = (Weight in grams) / (Atomic mass in amu) * (6.022 x 10^23 atoms/mol)
- Plugging in the values:
Number of gold atoms = (28.046055 g) / (196.967 amu) * (6.022 x 10^23 atoms/mol) - Calculating this gives 8.347 x 10^22 gold atoms
So there are approximately 8.347 x 10^22 gold atoms in 0.990 oz of pure gold.
Calculating the Number of Electrons
Now that we know the number of gold atoms, we can calculate the number of electrons by multiplying by 79, the atomic number of gold.
- Gold has an atomic number of 79, meaning each gold atom has 79 electrons
- Use the formula: Number of electrons = Number of atoms * 79 electrons per atom
- Plugging in the values:
Number of electrons = (8.347 x 10^22 atoms) * (79 electrons/atom) - Multiplying this out gives 6.594 x 10^24 electrons
Therefore, there are approximately 6.594 x 10^24 electrons in 0.990 oz of pure gold.
Conclusion
To summarize:
- There are 8.347 x 10^22 gold atoms in 0.990 oz of pure gold
- Each gold atom has 79 electrons
- By multiplying the number of atoms by 79, there are approximately 6.594 x 10^24 electrons in 0.990 oz of pure gold
This calculation provides an interesting way to visualize the enormous number of atoms and electrons in a small amount of a pure substance like gold. While 0.990 oz may seem tiny, it contains quadrillions and quadrillions of subatomic particles!
Detailed Step-by-Step Calculation
Here is a more detailed step-by-step overview of the full calculation:
1. Identify the Given Information
- 0.990 oz of pure gold
- 1 oz = 28.3495 g
- Atomic mass of gold = 196.967 amu
- Gold atomic number = 79 (79 electrons per Au atom)
2. Convert oz to grams
0.990 oz * (28.3495 g/oz) = 28.046055 g
3. Calculate the Number of Gold Atoms
Use the equation: Atoms = (Mass in g) / (Atomic mass in amu) * (6.022 x 10^23 atoms/mol)
Plugging in the values:
Number of Au atoms = (28.046055 g) / (196.967 amu) * (6.022 x 10^23 atoms/mol)
= 8.347 x 10^22 Au atoms
4. Multiply by 79 Electrons Per Atom to Get Total Electrons
Use the equation: Electrons = Atoms * (79 e-/atom)
Plugging in the values:
Number of electrons = (8.347 x 10^22 atoms) * (79 e-/atom)
= 6.594 x 10^24 electrons
Therefore, by carrying out this step-by-step calculation, we determine there are approximately 6.594 x 10^24 electrons in 0.990 oz of pure gold.
Electron Concepts and Calculations
Let’s take a deeper look at some of the key concepts and calculations related to electrons:
What is an Electron?
An electron is a subatomic particle that carries a negative electric charge. Electrons belong to the first generation of the lepton particle family and interact via the electromagnetic force. Electrons have an extremely small mass, almost 2000 times lighter than a proton.
Key Electron Facts:
- Charge: -1.602 x 10-19 C (elementary charge)
- Mass: 9.109 x 10-31 kg
- Spin: 1/2 spin
In atoms, electrons occupy a series of electron shells (labeled K, L, M, etc.) surrounding the nucleus. Each shell can hold a maximum number of electrons based on the quantum mechanical properties of the electron.
Calculating the Number of Electrons in an Atom
The number of electrons in a neutral atom is equal to its atomic number (Z). For example, gold has an atomic number of 79, which means a neutral gold atom contains 79 electrons. This can be summarized:
Number of electrons = Atomic number
The atomic number is the total number of protons in the atomic nucleus. Since a neutral atom contains equal protons and electrons, the atomic number gives the electron count.
Calculating Electrons in a Substance
To find the total number of electrons in a quantity of a substance, you first calculate the number of atoms, then multiply by the atomic number:
Total electrons = (Number of atoms) x (Atomic number)
The number of atoms can be derived from the mass and atomic mass using Avogadro’s number (6.022 x 10^23 atoms/mol).
Electron Charge and Electricity
The electron charge allows electrons to produce electricity in metals and semiconductors. Flowing electrons in a current produce electromagnet fields, which can perform work. Electron charges also facilitate chemical bonding between atoms.
Principle of Electric Charge Conservation
The total electric charge in an isolated system remains constant over time. This means the number of electrons lost in one place must equal the number gained somewhere else.
Other Key Facts About Electrons
- Electron shells fill in a fixed order: 1s, 2s, 2p, 3s, etc. following the Madelung rule
- Electrons have wavelike properties described by quantum physics
- Pauli Exclusion Principle states no two electrons can share the same quantum state
- Electrons flow between atoms in electrical conductors like metals
- The charge-to-mass ratio of the electron is -1.7588 x 10^11 C/kg
- Electrons have an intrinsic angular momentum called spin
Understanding the behaviors and properties of electrons is essential for fields like chemistry, materials science, engineering, and electronics. Even in a tiny amount of gold, the huge number of electrons reveals the vast scale and complexity of the quantum world.
Interesting Facts About Gold and Its Electrons
Here are some interesting additional facts about gold that provide context about its electrons:
- Gold is element Au on the periodic table, with atomic number 79
- Gold atoms form face-centered cubic crystals
- Gold is the most malleable and ductile metal
- Gold often occurs in free elemental form in nature
- Gold nanoparticles show quantum size effects
- 85% of the world’s gold has been mined since 1950
- Gold production is approximately 2500 tonnes per year globally
- Gold nanorods can be used for cancer treatment
- NASA uses a thin layer of gold on astronaut visors to reflect infrared radiation
- The gold in the FIFA World Cup trophy is worth over $150 million
The special properties of gold that depend on its electrons have made it highly valued throughout human history for applications like jewelry, currency, and electronics. Understanding the huge number of electrons even in a small amount of gold helps reveal why it is such a unique element.
Conclusions
To summarize key points:
- There are approximately 6.594 x 10^24 electrons in 0.990 oz of pure gold
- This is calculated from the number of gold atoms and atomic number 79
- Understanding electron calculations for atoms and compounds has broad scientific applications
- Gold’s electron configuration gives it special chemical and physical properties
- Subatomic particles like electrons exhibit complex quantum mechanical behaviors
Performing calculations like determining the number of electrons in a quantity of gold demonstrates the fascinating principles that govern electrons and their properties. The incredibly large numbers highlight the massive scales of the quantum world.
