The radioactive isotope Erbium160 has a halflife of 286 hour

The radioactive isotope Erbium-160 has a half-life of 28.6 hours. Find how long it will take for a sample to decay to 36% of its original mass. Round your answer to 2 decimal places.

Solution

decay constyant = 0.693/half life = 0.693/28.6 = 0.0242

Decay equation : N(t) = Noe^(-kt) where No is the intial amount

N(t) = 0.36No

So, 0.36No= Noe^(-0.0242t)

0.36 = e^(-0.0242t)

take natural log on both sides:

ln0.36 = -0.0242t

t = 42.22 hours