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?
○ 1
○ 5
○ 5.1
○ 5.44

Explanation:

Step1: Find initial mass of Ni - 59

The mass of Co - 59 is 5.27 g, which comes from decayed Ni - 59. The remaining Ni - 59 is 0.17 g. So initial mass \( m_0=0.17 + 5.27=5.44\) g.

Step2: Use half - life formula

The formula for radioactive decay is \( m = m_0(\frac{1}{2})^n\), where \( m\) is remaining mass, \( m_0\) is initial mass, \( n\) is number of half - lives.
We know \( m = 0.17\) g, \( m_0 = 5.44\) g. So \(\frac{m}{m_0}=\frac{0.17}{5.44}=\frac{1}{32}\).
And \(\frac{1}{32}=(\frac{1}{2})^n\), since \( 32 = 2^5\), then \((\frac{1}{2})^5=(\frac{1}{2})^n\), so \( n = 5\).

Answer:

5 (corresponding to the option "5")