Question

An 80.0 g sample of iodine-131 was placed in a sealed vessel forty days ago. Only 2.5 g of this isotope is now left. What is its half-life?

Answer 1

The answer is 8 days

Answer 2

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


`m_0=80 \ g \\ m=2.5 \ g \\ t=40 \ d \\ \\ 2.5=80 * ((1)/(2))^(40)/(T) \\ (2.5)/(80)=((1)/(2))^(40)/(T) \\ (1)/(32)=((1)/(2))^(40)/(T) \\ ((1)/(2))^5=((1)/(2))^(40)/(T) \\ 5=(40)/(T) \\ 5T=40 \\ T=(40)/(5) \\ T=8`

The half-life is 8 days.