Question

The half-life of U-238 is 4.5 x 10^9 years. How many disintegrations occur in 1 minute for a 10 mg sample of this element?

Answer 1

HL = 4.5*10^9

t = 1 min

m = 10 mg sample

so:

decay constant:

K = ln(2) / t1/2

t1/2 = ln(2) / K

t 1/2 = ln(2) / ( 4.5*10^9) = 1.54*10^-10 1/y

change to min

so

t 1/2 = 1.54*10^-10 1/y * 8760 h / y * 60 min /h

t 1/2 = 2.93*10^-16 min^-1

so..

for

m = 10 mg

change to mol

1mol of U = 235 g/mol

mol = mass/MW = (10*10^-3) / (235) = 4.26*10^-5

so

1 mol = 6.022*10^23 particles

4.26*10^-5 mol --> 4.26*10^-5)( 6.022*10^23

2.5653*10^19 atoms

so...

fr the distingrations:

Atoms / time = (2.56*10^19) * ( 2.93*10^-16) = 7.5*10^3 1/min

so

7500 atoms desintegrate per min