Question

One of the nuclides in spent nuclear fuel is U-235, an alpha emitter with a half-life of 703 million years. How long will it take for an amount of U-235 to reach 24.0% of its initial amount? Express your answer in years to three significant figures. View Available Hint(s)

Answer 1

Answer:

1447584654 years or 1.44 billion years

Explanation:

From the formula;

0.693/t1/2=2.303/t log No/N

Where;

t1/2 = half life of the U-235 nuclides

No= amount of U-235 initially present

N= amount of U-235 present after a time t

t= time taken for N amount of U-235 to remain

Since N= 0.24No

Substituting values

0.693/703×10^6 = 2.303/t log No/0.24No

9.8578×10^-10 = 2.303/t log 1/0.24

9.8578×10^-10 = 1.427/t

t= 1.427/9.8578×10^-10

t= 1447584654 years