Select the correct answer.

Which missing item would complete this alpha decay reaction?
[tex]\[
{}_{98}^{251}Cf \rightarrow {}_{96}^{247}Cm +
\][/tex]
A. \({}_{-1}^0\beta\)
B. \({}_{97}^{247}Bk\)
C. \({}_{2}^{4}He\)
D. \({}_{92}^{238}U\)
E. [tex]\({}_{0}^{0}\gamma\)[/tex]



Answer :

Let's solve the given alpha decay reaction step-by-step.

The reaction is:
[tex]\[ {}_{98}^{251} Cf \rightarrow {}_{96}^{247} Cm + \text{?} \][/tex]

1. Understanding Alpha Decay:
- Alpha decay is a type of radioactive decay where an alpha particle is emitted from a nucleus.
- An alpha particle is a helium-4 nucleus, denoted as \({}_2^4 He\).
- When an alpha particle is emitted, the parent nucleus loses 2 protons and 2 neutrons. This means:
- The atomic number decreases by 2.
- The mass number decreases by 4.

2. Determine the Change in Atomic Number and Mass Number:
- Initial atomic number of Californium (\(\text{Cf}\)): 98
- Final atomic number of Curium (\(\text{Cm}\)): 96
- Change in atomic number: \(98 - 96 = 2\)

- Initial mass number of Californium (\(\text{Cf}\)): 251
- Final mass number of Curium (\(\text{Cm}\)): 247
- Change in mass number: \(251 - 247 = 4\)

3. Comparison with Alpha Particle:
- An alpha particle has an atomic number of 2 and a mass number of 4.
- The changes we calculated (2 in atomic number and 4 in mass number) match those of an alpha particle.

4. Conclusion:
- The missing particle in the reaction must be an alpha particle \({}_2^4 He\).

Therefore, the correct answer is:
[tex]\[ \boxed{{}_2^4 He} \][/tex]
This corresponds to option C in the given choices.

Thus, the correct answer is:
C. [tex]\({}_2^4 He\)[/tex]