Question

Argon-39 has a half-life of 269 years. How long will it take for 52.5 g of a 60.0 g sample to decay to its daughter isotope?

Answer 1

`m=m_0 * ((1)/(2))^(t)/(T)`
m - the mass that remains unchanged, m₀ - the initial mass, t - time, T - the half-life


`T=269 \ years \\ m_0=60 \ g \\ m=60 \ g - 52.5 \ g=7.5 \ g \\ \\ 7.5 = 60 * ((1)/(2))^(t)/(269) \\ (7.5)/(60) = ((1)/(2))^(t)/(269) \\ (1)/(8)=((1)/(2))^(t)/(269) \\ ((1)/(2))^3 = ((1)/(2))^(t)/(269) \\ 3=(t)/(269) \\ 3 * 269=t \\ t=807`

It will take 807 years for 52.5 g of a 60 g sample to decay to its daughter isotope.