While making predictions about the outcome of an activity, or even planning for the outcome, exponential functions may be used to describe the some types of growth. Exponential growth is used to show the manner with which a quantity may increase over a specific period. The exponential function is modelled when the rate of change at a particular instant in time of a quantity is relative to the quantity in question.
Exponential growth may be used in the physics field of nuclear chain reactions , which is the basis of the modelling of nuclear reactors and weapons. During the reactions, an atom’s nucleus that undergoes fission produces neutrons , each of which can be absorbed by the adjacent atoms, which then results in their subsequent fission. Two neutrons which are released during the fission enable the chain reaction to ensue. Exponential functions depend on whether the probability of neutron absorption exceeds the probability of neutron escape, where if absorption occurs the production rate of neutrons and induced fissions increases exponentially in an uncontrolled reaction.
Delegate your assignment to our experts and they will do the rest.
The model for this problem is based on the factor of two, which is due to the result of the fission. In the first ‘generation’ (split), the atom is divided into two and the number of atoms fissioned increases on this factor i.e. the 5 th generation will have 16 fissioned atoms, which is 2 5 . This might be used to calculate the energy that would be emitted in a reaction if the amount of energy that is released by a single nucleus is known. For example if a scientist has a known amount of uranium mass, then they could calculate the number of atoms at their disposal. Assuming that all of the atoms would be fissioned, they might then calculate the number of generations that would result from this and also the amount of energy released due to the reaction. This information could be used to determine the potency of the bomb and approximate its effect.
