Question

The half life of a specific Tc-99m is 6 hours. How much of an 192 mg sample will have decayed after 30 hours? 186 mg 32 mg 6 mg 160 mg The answer is : 186 mg. Why?

Answer 1

After every half life (6hrs) number of radioactive nuclide decrease to its half value.

Number of nuclide is proportional to mass of radio active material. Let initially there were N_o active nuclides.

Concentration = C_o/2ⁿ where n = number of half lives

= time /t_50%

After 6 hours radi active nuclide becomes N_o/2

After 12 hours radio active nuclide becomes N_o/2²

After 18 hours radio active nuclide becomes N_o^{​​​​​​}/2³

After 24 hours radio active nuclide becomes N_o/2⁴

After 30 hours radio active nuclide becomes N_o/2⁵

N_o =( 192×10^-3/(atomic mass))N_a where N_a is Avogadro number.

N = N_o/ 32

Mass of sample left after 30 hours = 192÷32 = 6mg

Mass of sample decayed after 30 hours = 192-6 = 186mg