Answer :
To determine what indicates that transmutation has taken place in the following nuclear reaction:
[tex]\[ { }_{96}^{242} \text{Cm} \rightarrow { }_{94}^{238} \text{Pu} + { }_2^4 \text{He} \][/tex]
Let's analyze the reaction step-by-step.
### Understanding the Reactants and Products:
- Curium-242 ([tex]\( \text{Cm-242} \)[/tex]) is the initial nucleus. It has:
- Atomic number [tex]\( Z = 96 \)[/tex] (number of protons)
- Mass number [tex]\( A = 242 \)[/tex] (number of protons + neutrons)
- Plutonium-238 ([tex]\( \text{Pu-238} \)[/tex]) is one of the products. It has:
- Atomic number [tex]\( Z = 94 \)[/tex]
- Mass number [tex]\( A = 238 \)[/tex]
- Helium-4 ([tex]\( \text{He-4} \)[/tex]) is another product, also known as an alpha particle. It has:
- Atomic number [tex]\( Z = 2 \)[/tex]
- Mass number [tex]\( A = 4 \)[/tex]
### Conservation Laws:
1. Conservation of Atomic Number:
- On the left side of the equation:
[tex]\[ 96 \ (\text{Curium}) \][/tex]
- On the right side of the equation:
[tex]\[ 94 \ (\text{Plutonium}) + 2\ (\text{Helium}) = 96 \][/tex]
The atomic number is conserved.
2. Conservation of Mass Number:
- On the left side of the equation:
[tex]\[ 242 \ (\text{Curium}) \][/tex]
- On the right side of the equation:
[tex]\[ 238 \ (\text{Plutonium}) + 4 \ (\text{Helium}) = 242 \][/tex]
The mass number is also conserved.
### Identifying Transmutation:
Transmutation refers to the process where the nucleus of one element changes into the nucleus of another element. Let's see how this applies to the given reaction:
- Curium-242 (an element with atomic number 96) changes and produces:
- Plutonium-238 (an element with atomic number 94)
- Helium-4 (an element with atomic number 2)
Since we see a change in the identities of the nuclei involved (from curium to plutonium and helium), this is a clear example of transmutation.
### Evaluating the Choices:
- Option A: The number of atoms is conserved, but the number of nucleons is not.
- Incorrect: Both number of nucleons and number of atoms are conserved.
- Option B: The nucleus of an atom changes.
- Correct: The transformation from Curium-242 to Plutonium-238 and Helium-4 is a change in the nucleus.
- Option C: There is conservation of both nucleons and atoms.
- While this is true based on conservation laws, it is not specifically indicating transmutation.
- Option D: It involves more than one element.
- This is true but does not directly explain transmutation as clearly as Option B does.
Given these analyses, the best explanation indicating that transmutation has taken place is:
[tex]\[ \boxed{\text{B}} \][/tex]
Therefore, the correct choice is B: "The nucleus of an atom changes."
[tex]\[ { }_{96}^{242} \text{Cm} \rightarrow { }_{94}^{238} \text{Pu} + { }_2^4 \text{He} \][/tex]
Let's analyze the reaction step-by-step.
### Understanding the Reactants and Products:
- Curium-242 ([tex]\( \text{Cm-242} \)[/tex]) is the initial nucleus. It has:
- Atomic number [tex]\( Z = 96 \)[/tex] (number of protons)
- Mass number [tex]\( A = 242 \)[/tex] (number of protons + neutrons)
- Plutonium-238 ([tex]\( \text{Pu-238} \)[/tex]) is one of the products. It has:
- Atomic number [tex]\( Z = 94 \)[/tex]
- Mass number [tex]\( A = 238 \)[/tex]
- Helium-4 ([tex]\( \text{He-4} \)[/tex]) is another product, also known as an alpha particle. It has:
- Atomic number [tex]\( Z = 2 \)[/tex]
- Mass number [tex]\( A = 4 \)[/tex]
### Conservation Laws:
1. Conservation of Atomic Number:
- On the left side of the equation:
[tex]\[ 96 \ (\text{Curium}) \][/tex]
- On the right side of the equation:
[tex]\[ 94 \ (\text{Plutonium}) + 2\ (\text{Helium}) = 96 \][/tex]
The atomic number is conserved.
2. Conservation of Mass Number:
- On the left side of the equation:
[tex]\[ 242 \ (\text{Curium}) \][/tex]
- On the right side of the equation:
[tex]\[ 238 \ (\text{Plutonium}) + 4 \ (\text{Helium}) = 242 \][/tex]
The mass number is also conserved.
### Identifying Transmutation:
Transmutation refers to the process where the nucleus of one element changes into the nucleus of another element. Let's see how this applies to the given reaction:
- Curium-242 (an element with atomic number 96) changes and produces:
- Plutonium-238 (an element with atomic number 94)
- Helium-4 (an element with atomic number 2)
Since we see a change in the identities of the nuclei involved (from curium to plutonium and helium), this is a clear example of transmutation.
### Evaluating the Choices:
- Option A: The number of atoms is conserved, but the number of nucleons is not.
- Incorrect: Both number of nucleons and number of atoms are conserved.
- Option B: The nucleus of an atom changes.
- Correct: The transformation from Curium-242 to Plutonium-238 and Helium-4 is a change in the nucleus.
- Option C: There is conservation of both nucleons and atoms.
- While this is true based on conservation laws, it is not specifically indicating transmutation.
- Option D: It involves more than one element.
- This is true but does not directly explain transmutation as clearly as Option B does.
Given these analyses, the best explanation indicating that transmutation has taken place is:
[tex]\[ \boxed{\text{B}} \][/tex]
Therefore, the correct choice is B: "The nucleus of an atom changes."
