Question

This question is about graph of rock clock

Explain what each symbol represents in the equation

Example:

Wavelength represent?

t = time

87 yrs38 The slope of the line gives you the time since crystallization. The slope of the isochron increases with time (t). later 87Sr 86 0 87Rb 86Sr minerals with more As the rock ages, the initial rubidium accumulate more 87Sr. rock, regardless of the proportion of rubidium to strontium. The values form a straight horizontal line, called an isochron. D: As the strontium-87 decays, the ratios change, increasing the slope of the

Answer 1

This is the equation of radioactive decay and can be represented as-

- dN / dt = $\lambda$ N

The sign on the left hand is negative because the number of nuclei is decreasing.

dN / N = $\lambda$ dt

and integrating yields - ln N = $\lambda$ t + C

C is the integration constant. We solve for C by putting N = N0 and t = t0 .

Then C = - ln N0

Substituting for C gives - ln N = $\lambda$ t – ln N0

ln N – ln N0 = – $\lambda$ t

ln N/N0 = – $\lambda$ t

Eliminate the natural log -

N/N0 = e - $\lambda$ t

N = N0 e - $\lambda$ t

Let`s say decayed N have produced radiogenic daughters D*-

D* = N0 – N

Replacing N0 with Ne ^{$\lambda$ t} yields-

D* = N e   ^{$\lambda$ t} - N

D* = N (e   ^{$\lambda$ t} – 1)

The number of daughter isotopes is the sum of those initially present plus those radiogenically produced.

D = D0 + D*

D = D0 + N (e   ^{$\lambda$ t} – 1)

This is the basic radioactive decay equation used for determining ages of rocks.