Question

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:

Answer 1

756.6 years.

Step-by-step 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