Well, when it comes to slowing down neutrons, it's like trying to slow down a toddler on a sugar rush - not an easy task! Now, let's calculate the ratio of a neutron's final kinetic energy to its initial kinetic energy for each of the targets you mentioned:
A) An electron. Now, electrons might be small, but they can pack a punch (or a tiny kick). Given the mass of a neutron and the mass of an electron, the ratio of final kinetic energy to initial kinetic energy, Kf/Ki, will be less than 1. So, let's just say that an electron is like trying to slow down a neutron with a feather.
B) A proton. Ah, now we're talking about the big leagues! Protons have a similar mass to neutrons, so when they collide head-on, they can transfer a significant amount of their energy. Therefore, the ratio of final kinetic energy to initial kinetic energy, Kf/Ki, will be close to 1. Protons are like those enthusiastic cheerleaders, ready to boost the neutron's energy and keep the reaction going!
C) The nucleus of a lead atom. Whoa, talk about heavyweight! The nucleus of a lead atom is massive compared to a neutron. When a neutron smacks into it head-on, it's like hitting a brick wall! In this case, the ratio of final kinetic energy to initial kinetic energy, Kf/Ki, will be very small, approaching 0. Those lead nuclei are like the granddaddies of slowing down neutrons, taking away their energy faster than a whirlwind!
So, in summary, the electron is like a feather, the proton is like a cheerleader, and the lead nucleus is like a brick wall when it comes to slowing down neutrons.