How many coulombs of charge are on the electrons in a nickel coin? Follow this method to find the answer.
a. Find the number of atoms in a nickel coin. A nickel coin has a mass of about 5 g. Each mole (6.02 x 1023 atoms) has a mass of about 58 g.
b. Find the number of electrons in the coin. Each nickel atom has 28 electrons.
c. Find how many coulombs of charge are on the electrons.
The Correct Answer and Explanation is :
Let’s go step by step to find the number of coulombs of charge on the electrons in a nickel coin.
a. Find the number of atoms in a nickel coin
We are given that the mass of a nickel coin is about 5 grams and the molar mass of nickel is 58 grams per mole.
First, we can find the number of moles of nickel in the coin:
[
\text{moles of nickel} = \frac{\text{mass of coin}}{\text{molar mass of nickel}} = \frac{5 \, \text{g}}{58 \, \text{g/mol}} = 0.0862 \, \text{mol}
]
Now, using Avogadro’s number (which is (6.02 \times 10^{23}) atoms per mole), we can find the number of atoms in the nickel coin:
[
\text{Number of atoms} = 0.0862 \, \text{mol} \times 6.02 \times 10^{23} \, \text{atoms/mol} = 5.19 \times 10^{22} \, \text{atoms}
]
b. Find the number of electrons in the coin
Each nickel atom has 28 electrons. So, the total number of electrons in the nickel coin is:
[
\text{Number of electrons} = 5.19 \times 10^{22} \, \text{atoms} \times 28 \, \text{electrons/atom} = 1.45 \times 10^{24} \, \text{electrons}
]
c. Find how many coulombs of charge are on the electrons
Each electron carries a charge of (1.6 \times 10^{-19}) coulombs. So, the total charge on all the electrons in the coin is:
[
\text{Total charge} = 1.45 \times 10^{24} \, \text{electrons} \times 1.6 \times 10^{-19} \, \text{C/electron} = 2.32 \times 10^{5} \, \text{C}
]
Final Answer:
The total charge on the electrons in a nickel coin is approximately (2.32 \times 10^{5} \, \text{C}).
Explanation:
The problem uses the fundamental relationship between the mass of an object, the number of atoms in it, and the charge carried by electrons. First, by using the molar mass of nickel and Avogadro’s number, we determined the number of atoms in a 5-gram coin. Then, since each nickel atom contains 28 electrons, we multiplied the number of atoms by 28 to find the total number of electrons. Finally, multiplying the total number of electrons by the charge of a single electron gave us the total charge in coulombs.
This method relies on fundamental concepts of stoichiometry (to convert mass into moles), atomic structure (to determine the number of electrons), and electrostatics (to calculate the total charge). The final result, (2.32 \times 10^{5} \, \text{C}), illustrates how much charge is carried by the electrons in the coin, which is a large number due to the immense number of electrons present in even a small amount of matter.