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

B. 5

Step-by-step 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 = (t_(1/2))/(\ln 2)`

`\tau = (76000\,yr)/(\ln 2)`

`\tau = 109644.823\,yr`

The decayment rate is given the following expression:

`(m)/(m_(o)) = e^{-(t)/(\tau) }`

`\ln (m)/(m_(o)) = -(t)/(\tau)`

`t=-\tau \cdot \ln (m)/(m_(o))`

`t = -(109644.823\,yr)\cdot \ln (0.17\,g)/(5.44\,g)`

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

Answer 2

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