Which statements about nuclear fission and nuclear fusion are true? Select the two correct answers.

a. they both release large amounts of energy
b. they both involve two atoms fusing into one atom
c. they both involve one atom splitting into two atoms
d. they both occur in the nucleus of an atom

The correct answers are:

a. they both release large amounts of energy
c. they both involve one atom splitting into two atoms

The correct answers are:

a. they both release large amounts of energy
c. they both involve one atom splitting into two atoms

To determine which statements about nuclear fission and nuclear fusion are true, we need to understand the concepts of each.

1. Nuclear fission:
Nuclear fission involves the splitting of an atom's nucleus into two smaller nuclei. This process releases a large amount of energy. Each of the two smaller nuclei also releases additional neutrons, which can then go on to split other nuclei, resulting in a chain reaction.

2. Nuclear fusion:
Nuclear fusion involves the combining of two smaller atomic nuclei to form a larger nucleus. This process also releases a large amount of energy. Fusion is the process that powers the sun.

Let's evaluate each statement:

a. They both release large amounts of energy.
This statement is true. Both nuclear fission and fusion reactions release a significant amount of energy.

b. They both involve two atoms fusing into one atom.
This statement is false. Nuclear fusion involves the fusion of two atomic nuclei to form a larger nucleus but not just into one atom.

c. They both involve one atom splitting into two atoms.
This statement is true for nuclear fission. In a fission reaction, a single atom's nucleus splits into two smaller nuclei. However, it is not true for nuclear fusion.

d. They both occur in the nucleus of an atom.
This statement is true for both nuclear fission and fusion. Both processes involve changes in the nucleus of an atom.

Therefore, the correct statements are:
a. They both release large amounts of energy.
c. They both involve one atom splitting into two atoms.