The decay constant of ¹⁹⁷₈₀ Hg (which decays by electron capture to ¹⁹⁷₇₉ Au ) is 1.8 10⁻⁴ s ⁻¹ . Determine the average-life of this isotope.

Step-by-step solution

The average life of a radioactive isotope is given by the reciprocal of its decay constant . = 1 Given = 1.8 10⁻⁴ s ⁻¹ , substituting this value gives: = 1 1.8 10⁻⁴ s = 10000 1.8 s = 50000 9 s To convert the average life from seconds to minutes, divide by 60 : = 50000 9 60 min = 2500 27 min 92.59 min 92.6 min