a) How many electrons are necessary to produce a charge of -1.2 C? Express your answer using two significant figures.ÂÂ
b) What is the mass of this many electrons? Express your answer using two significant figures.ÂÂ
The Correct Answer and Explanation is :
a) Number of Electrons Needed to Produce a Charge of -1.2 C
The charge of a single electron is given as:
[
e = -1.6 \times 10^{-19} \, \text{C}
]
To calculate the number of electrons required to produce a total charge of -1.2 C, we use the following formula:
[
Q = n \times e
]
Where:
- ( Q ) is the total charge (given as -1.2 C),
- ( n ) is the number of electrons, and
- ( e ) is the charge of a single electron.
Rearranging the formula to solve for ( n ):
[
n = \frac{Q}{e}
]
Substitute the values:
[
n = \frac{-1.2 \, \text{C}}{-1.6 \times 10^{-19} \, \text{C}}
]
Calculating:
[
n = 7.5 \times 10^{18} \, \text{electrons}
]
Thus, the number of electrons needed to produce a charge of -1.2 C is:
[
n = 7.5 \times 10^{18} \, \text{electrons}
]
b) Mass of These Electrons
The mass of a single electron is:
[
m_e = 9.11 \times 10^{-31} \, \text{kg}
]
To find the total mass of the electrons, we multiply the number of electrons by the mass of a single electron:
[
\text{Total mass} = n \times m_e
]
Substitute the values:
[
\text{Total mass} = (7.5 \times 10^{18}) \times (9.11 \times 10^{-31} \, \text{kg})
]
Calculating:
[
\text{Total mass} = 6.83 \times 10^{-12} \, \text{kg}
]
Thus, the mass of the electrons is:
[
\text{Total mass} = 6.8 \times 10^{-12} \, \text{kg}
]
Summary:
- The number of electrons needed to produce a charge of -1.2 C is approximately ( 7.5 \times 10^{18} ) electrons.
- The mass of these electrons is approximately ( 6.8 \times 10^{-12} \, \text{kg} ).
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Here is the visual representation of the calculations for determining the number of electrons and their mass in the scenario of producing a charge of -1.2 C. It includes the relevant formulas and steps to illustrate the process. Let me know if you need further clarification!