In this equation, what shows that transmutation has taken place?

[tex]{}_{96}^{242} Cm \rightarrow {}_{94}^{238} Pu + {}_2^4 He[/tex]

A. The number of atoms is conserved, but the number of nucleons is not.
B. The nucleus of an atom changes.
C. There is conservation of both nucleons and atoms.
D. It involves more than one element.



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."