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?

Total amount of nickel when meteorite was formed m_i = 0.17 + 5.27 = 5.44 g

number of half lives passed = n

final mass of nickel m_f = 0.17

m_f = m_i / (2^n)

m_i/m_f = 2^n

ln (m_i/m_f) = n ln (2)

n = ln (m_1/m_f) / ln (2)

number of half lives n = ln (5.44/0.17) / ln (2) = 5