It’s Sunday: what better day to learn some nuclear physics, right? Especially, how to make a nuclear bomb!
What you do is get a lump of purified uranium-235 (U-235) and fire one neutron at it at very high-speed — at about 90pc the speed of light. When the neutron comes into contact with the U-235 atom, it splits
it into two smaller atoms in a process that also generates huge amounts of energy and three fast-moving neutrons.
The three new neutrons will each strike another U-235 atom to generate even more energy and nine addition neutrons – three from each strike. These nine will do the same and produce much more energy
plus 27 neutrons...and so on.
This is technically known as a nuclear chain-reaction and it happens very fast — within a billionth of a second, trillions of U-235 atoms will have been split and all we will see is one great explosion!
The important point to take home toay is that the rate at which the U-235 atoms are consumed is proportional to the number that has already been consumed. For many centuries, mathematicians have known
about these kinds of processes and have even given them a special name – exponential functions.
An exponential process is one in which the rate of change is proportional to the amount of change that has already occurred. A good example of this is the simple case of an accelerating object. The speed is
continuously increasing. That is, the rate of change of distance with respect to time (otherwise known as speed) increases as the object moves farther away from the starting point.
SITUATION APPROACHING EXPONENTIAL REALM
If we are not careful, an exponential process can quickly get out of control; like happens during a melt-down in a nuclear power station. I fear that our traffic situation is now approaching the exponential
realm. People are gradually beginning to buy new cars.
This is how: suppose you moved into a new neighbourhood that has, say, 100 households, of which 50 have cars. The access roads will be fairly open. However, in about three to five years, everyone will
have a car — thanks you the growing economy.
By that time you will have noticed that you need to wake up earlier in order to complete the morning circuit of dropping children in school, taking your spouse to work and getting to your office on time.
When the wake-up time becomes unreasonable, you decide to buy a second car: you use one to drop the children in school and the spouse takes the other to work. Soon enough, your neighbours will copy
you and before you know it there will be 200 cars in your estate!
Still the problem persists and you decide to buy a third car to take children to school. Now you are buying cars because there are too many cars on the road – the more the traffic, the more you buy!
This is the beginning of an exponential growth and before long the traffic problem will “explode” like a nuclear bomb.