Explanation:

1. Understanding Nuclear Fission:
Nuclear fission is a process in which the nucleus of an atom splits into two smaller nuclei, releasing a large amount of energy. In this process, one atom of a heavy element, such as uranium-235 (92U235), absorbs a neutron and becomes unstable. This unstable nucleus then undergoes fission, resulting in the formation of two smaller nuclei, such as xenon-142 (54Xe142) and strontium-90 (38Sr90), along with the release of several neutrons.

2. Calculation of Neutrons Emitted:
To calculate the number of neutrons emitted during nuclear fission, we need to consider the conservation of mass and charge. The number of protons and neutrons on each side of the equation must be equal.

2.1. Initial Nucleus:
The initial nucleus is uranium-235 (92U235), which has 92 protons and 143 neutrons.

2.2. Final Nuclei:
The final nuclei are xenon-142 (54Xe142) and strontium-90 (38Sr90).

2.2.1. Xenon-142 (54Xe142):
The number of protons in xenon-142 is 54, so the number of neutrons must be 142 - 54 = 88.

2.2.2. Strontium-90 (38Sr90):
The number of protons in strontium-90 is 38, so the number of neutrons must be 90 - 38 = 52.

2.3. Calculation:
To calculate the number of neutrons emitted, we subtract the total number of neutrons in the final nuclei from the total number of neutrons in the initial nucleus.

Total neutrons in the final nuclei = 88 (neutrons in xenon-142) + 52 (neutrons in strontium-90) = 140.

Neutrons emitted = Total neutrons in the initial nucleus - Total neutrons in the final nuclei = 143 - 140 = 3.

Therefore, the correct answer is 3 neutrons emitted during the controlled nuclear fission of uranium-235 (92U235) to xenon-142 (54Xe142) and strontium-90 (38Sr90).