Lt takes 4 hr 39 min for a 2.00-mg sample of radium-230 to decay to 0.25 mg. what is the half-life of radium-230?

Radioactive decay = > C = Co { e ^ ( - kt) |

dа ta:

Co = 2.00 mg

C = 0.25 mg

t = 4 hr 39 min

Time conversion: 4 hr 39 min = 4.65 hr

1) Replace the data in the equation to find k

C = Co { e ^ (-kt) } = > C / Co = e ^ (-kt) = > - kt = ln { C / Co} = > kt = ln {Co / C}

=> k = ln {Co / C} / t = ln {2.00mg / 0.25mg} / 4.65 hr = 0.44719

2) Use C / Co = 1/2 to find the hallf-life

C / Co = e ^ (-kt) = > - kt = ln (C / Co)

=> - kt = ln (1/2) = > kt = ln (2) = > t = ln (2) / k

t = ln (2) / 0.44719 = 1.55 hr.

Answer: 1.55 hr