Write an expression for the net change in charge if two electrons are added to each of six atoms in a group. Also, write an expression that represents removing two protons each from a group of six atoms.
The Correct Answer and Explanation is:
To solve this, we need to express the net change in charge resulting from the addition of electrons and the removal of protons from a group of atoms. Here’s how we can approach each part of the question:
1. Net Change in Charge from Adding Electrons
Each electron carries a negative charge of ( -1 \, e ) (where ( e ) is the elementary charge, approximately ( 1.602 \times 10^{-19} ) coulombs). If two electrons are added to each of six atoms, the total change in charge can be expressed as:
[
\text{Net change in charge} = (\text{number of electrons added}) \times (\text{charge of each electron})
]
Since two electrons are added to each atom, and there are six atoms in total, the total number of electrons added is:
[
2 \times 6 = 12 \, \text{electrons}
]
The charge contributed by each of these 12 electrons is ( -1 \, e ). Therefore, the total change in charge is:
[
\text{Net change in charge} = 12 \times (-1 \, e) = -12 \, e
]
Thus, the expression for the net change in charge from adding two electrons to each of six atoms is:
[
\boxed{-12e}
]
This means the charge of the group of atoms becomes more negative, with a total charge change of ( -12 \, e ).
2. Net Change in Charge from Removing Protons
Each proton carries a positive charge of ( +1 \, e ). If two protons are removed from each of six atoms, the total number of protons removed is:
[
2 \times 6 = 12 \, \text{protons}
]
Since each proton carries a positive charge of ( +1 \, e ), the total change in charge is:
[
\text{Net change in charge} = 12 \times (+1 \, e) = +12 \, e
]
Thus, the expression for the net change in charge from removing two protons from each of six atoms is:
[
\boxed{+12e}
]
This means the group of atoms becomes more positive, with a total charge change of ( +12 \, e ).
Explanation
The change in charge of an atom depends on the type of particle added or removed. Electrons have a negative charge, so adding electrons makes the atom more negatively charged. Conversely, protons have a positive charge, so removing protons makes the atom more positively charged. In this problem:
- Adding electrons: Each electron adds ( -1 \, e ) of charge. With two electrons added to each of six atoms, the total charge change is ( -12 \, e ).
- Removing protons: Each proton has a ( +1 \, e ) charge. With two protons removed from each of six atoms, the total charge change is ( +12 \, e ).
These calculations rely on the fact that the number of electrons and protons determines the overall charge of an atom or a group of atoms.