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Answer :
Certainly! Let's solve this step-by-step:
1. Identify the Element and Its Characteristics:
- The element in question is Barium (symbol: Ba).
- The isotope is [tex]\( ^{138}\text{Ba}^{2+} \)[/tex], which indicates:
- A mass number of 138. This is the total number of protons and neutrons.
- A [tex]\( 2+ \)[/tex] charge, meaning it has lost 2 electrons.
2. Determine the Number of Protons:
- The atomic number of Barium (Ba) is 56. This means there are 56 protons in a Barium atom.
3. Calculate the Number of Neutrons:
- The number of neutrons is found by subtracting the number of protons from the mass number.
[tex]\[
\text{Neutrons} = \text{Mass Number} - \text{Protons} = 138 - 56 = 82
\][/tex]
- So, there are 82 neutrons.
4. Determine the Number of Electrons:
- In a neutral Barium atom, there would be 56 electrons to balance the 56 protons.
- Since the ion is [tex]\( \text{Ba}^{2+} \)[/tex], it has lost 2 electrons.
[tex]\[
\text{Electrons} = \text{Protons} - \text{Charge} = 56 - 2 = 54
\][/tex]
- So, there are 54 electrons.
5. Conclusion:
- Therefore, the total numbers are: 82 neutrons, 56 protons, and 54 electrons.
This corresponds to option D, which states: 82 neutrons, 56 protons, 54 electrons.
1. Identify the Element and Its Characteristics:
- The element in question is Barium (symbol: Ba).
- The isotope is [tex]\( ^{138}\text{Ba}^{2+} \)[/tex], which indicates:
- A mass number of 138. This is the total number of protons and neutrons.
- A [tex]\( 2+ \)[/tex] charge, meaning it has lost 2 electrons.
2. Determine the Number of Protons:
- The atomic number of Barium (Ba) is 56. This means there are 56 protons in a Barium atom.
3. Calculate the Number of Neutrons:
- The number of neutrons is found by subtracting the number of protons from the mass number.
[tex]\[
\text{Neutrons} = \text{Mass Number} - \text{Protons} = 138 - 56 = 82
\][/tex]
- So, there are 82 neutrons.
4. Determine the Number of Electrons:
- In a neutral Barium atom, there would be 56 electrons to balance the 56 protons.
- Since the ion is [tex]\( \text{Ba}^{2+} \)[/tex], it has lost 2 electrons.
[tex]\[
\text{Electrons} = \text{Protons} - \text{Charge} = 56 - 2 = 54
\][/tex]
- So, there are 54 electrons.
5. Conclusion:
- Therefore, the total numbers are: 82 neutrons, 56 protons, and 54 electrons.
This corresponds to option D, which states: 82 neutrons, 56 protons, 54 electrons.
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