Technetium99m an important radionuclide in medicine has a ha

Technetium-99m, an important radionuclide in medicine, has a half-life of 6.0 hours. What percentage of a sample of technetium-99m will remain undecayed after the following times?

Solution

k = 0.693/(half life)
= 0.693/6.0
= 0.1155 hours^-1

use,
ln([A]/[A0]) = -k*t

t = 12.0 hours
ln([A]/[A0]) = -0.1155*12.0
ln([A]/[A0]) = -1.386
[A]/[A0] = 0.25

in percentage 25 %

t = 1 day
= 24.0 hours
ln([A]/[A0]) = -0.1155*24.0
ln([A]/[A0]) = -2.772
[A]/[A0] = 0.0625

in percentage 6.25 %

t = 5 half life
= 5*6
= 30.0 hours
ln([A]/[A0]) = -0.1155*30.0
ln([A]/[A0]) = -3.465
[A]/[A0] = 0.0313

in percentage 3.13 %