I need answers for only the bold font questions, but I need the steps. Consider

ID: 2269816 • Letter: I

Question

I need answers for only the bold font questions, but I need the steps.

Consider radioactive 40K (21 protons, 19 neutrons). About 10.72% of the time, it

spontaneously decays to 40Ar (20 protons and 20 neutrons). The half-life for this process is

1.25E9 yr. If Z is the mass of a radioactive element, then an expression that describes

the rate of decay, dZ=dt is:

dZ/dt = -CZ (1)

where C is a constant. What are the units of C? What is the relationship between C and

the half-life?

The Earth has a total mass of 5.97E24 kg and 1.7E-4 of the Earth's mass

is potassium. Approximately, 0.012% of the Earth's potassium is 40K. How much 40K

currently is contained within the Earth? If the Earth has an age of 4.6E9 yr, how much

40K was present when the Earth formed?

The mass of 40Ar in the Earth's atmosphere is 6.6E16 kg or about 1% of the

atmosphere's total mass. How does this mass of 40Ar compare to the amount that would

be expected from the radioactive decay of the initial 40K in the Earth's interior and the

presumption that 50% has outgassed in volcanos?

Unit of C = sec^-1

Relationship is : t(half) = ln2/c = 0.693/c

amount of 40K within the earth = (5.97 * E24) * (1.7 * E-4) * 0.00012 = 590872.98 kg

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