Question

Uranium-235 has a half-life of 700 million years. How long does it take a 100-gram sample of Uranium-235 to decay to a mass of 50 grams?

Answer 1

Answer:

7.001486672 × 10^8 years

Explanation:

The formula for getting the remaining amount of substance after decay is given by :

N = N0 e^-kt

N = Remaining amount at time t.

k = The disintegration constant

t = time period of disintegration.

k = ln 2 / half life

k = ln 2/700000000 = 9.90 × 10^-10

50 = 100e{-9.90 × 10^-10t}

50/100 = e{-9.90 × 10^-10t}

Taking ln on both sides we have :

ln 0.5 = - 9.90 × 10^-10 t

-0.693147 = - 9.90 × 10^-10t

t = (-0.693147/-9.90 × 10^-10)

t = 700148667.2

t = 7.001486672 × 10^8 years.

This is the time it takes Uranium to decay from 100 to 50 grams.