A zircon mineral is found in the North Cascades and used to date the age of the mountains. The sample is treated and the relative amount of 235U and 207Pb are evaluated by mass spectroscopy. The number of atoms found are:

756.6 years.

Explanation:

Carbon dating is the process of measuring carbon - 13 of a dead object or substance in order to determine the age of the object or substance. This question is about radionuclide dating. The number of nuclei in a radioactive substance disintegrate in a decreasing exponentially manner with time.

In order to determine the age of the North Cascades we will be using the formula below;

Age, t= 1/ λ × [ ln (1 + Dt/pt). (1).

Also, λ = ln 2/ t(1/2).

Where t(1/2) is the half life, Dt and pt are the numbers of daughter atoms and the numbers of parent atoms respectively. The assumption is that there are no daughter atoms initially at time, t= 0 and daughter atoms are due to the parent atoms decay.

Hence, λ = ln 2 / 10.= 0.69315/10 = 0.07 yr^-.

So, using equation (1) above we will have;

Age,t = 1/ 0.07 [ ln (1 + 3.93 × 10^11/ 4.15 × 10^12) ].

Age, t = 14.3 [ ln (1 + 9.5 ×10^22)].

Age, t= 14.3 × 52.91.

Age,t = 756.6 years

it is the minimum amount of material needed to sustain a fission reaction.

critical mass is the minimum amount of fissionable material that must be assembled for a sustained fission reaction to take place. although two to three neutrons are produced for every fission, not all of these neutrons are available for continuing the fission reaction. if the conditions are such that the neutrons are lost at a faster rate than they are formed by fission, the chain reaction will not be self-sustaining.   at the point where the chain reaction can become self-sustaining, this is referred to as critical mass.