Question

If 0.04625 mg. of Uranium-235 remains after 2.8 x 10^9 years, what was

the original mass of the sample of Uranium-235? The half-life of Uranium-235 is 7.0 x 10^8 years.

Answer 1

Answer: The original mass of the sample of Uranium-235 is 0.7308 mg

Step-by-step explanation:

Expression for rate law for first order kinetics is given by:

`t=(2.303)/(k)\log(a)/(a-x)`

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process

a) for calculating rate constant

`t_{(1)/(2)}=(0.693)/(k)`

`k=(0.693)/(7.0* 10^8years)=0.099* 10^(-8)years^(-1)`

b) for time of
`2.8* 10^9` years

`2.8* 10^9=(2.303)/(0.099* 10^(-8))\log(a)/(0.04625)`

`\log(a)/(0.04625)=1.2`

`(a)/(0.04625)=15.8`

`a=0.7308mg`

The original mass of the sample of Uranium-235 is 0.7308 mg