An unknown radioactive element decays into nonradioactive su

An unknown radioactive element decays into non-radioactive substances In 560| days the radioactivity of a sample decreases by 26| percent What is the half-life of the element? How long will it take for a sample of 100| mg to decay to 68| mg? time needed (days)

Solution

Exponential function : m = mo*e^(-t/T)

(1 - 0.26) = e^(-560/T)

0.74 = e^(-560/T)

1/0.74 = e^(5620/T)

ln (1/0.74) = 560/T

T = 560/(ln(1/0.74)) = 1859.82 days

h = half life

0.5 = e^(-h/T)

2 = e^(h/T)

h/T = ln (2)

h = T*ln 2 = 1859.82*ln 2 = 1289.13 days...the half life

For 100 g to decay to 68 g

0.68 = e^(-t/T)

ln (0.68) = (-t/T)

t = -T*ln (0.68) =-1859.82*ln (0.68)

t = 717.26 days..time for 100 g to delay 68 g