Question

A meteorite contains 0.17 g of nickel-59, a radioisotope that decays to form cobalt-59. The meteorite also contains 5.27 g of cobalt-59. How many nickel-59 half-lives have passed since the meteorite formed?

A. 1
B. 5
C. 5.1
D. 5.44

Answer 1

If all the ⁵⁹Co came from ⁵⁹Ni, ½ʰ = 0.17/(0.17 + 5.27) = 0.03125. Then h, the number of half lives, = 5.

B. 5

Answer 2

Answer:

B. 5

Explanation:

The half-life of the nickel-59 is 76000 years. The initial mass of the radioisotope is:

$m_{o} = 5.44\,g$

The time constant for the radioisotope is:

$\tau = \frac{t_{1/2}}{\ln 2}$

$\tau = \frac{76000\,yr}{\ln 2}$

$\tau = 109644.823\,yr$

The decayment rate is given the following expression:

$\frac{m}{m_{o}} = e^{-\frac{t}{\tau} }$

$\ln \frac{m}{m_{o}} = -\frac{t}{\tau}$

$t=-\tau \cdot \ln \frac{m}{m_{o}}$

$t = -(109644.823\,yr)\cdot \ln \frac{0.17\,g}{5.44\,g}$

$t = 380000\,yr$ (5 half-lives).