Uranium-235 has a half-life of 710 million years. If it is determined that a certain amount of stored U-235 will be considered safe only when its radioactivity has dropped to 0.10 percent of the original level, approximately how much time must the U-235 be stored securely to be safe?

(A) 7.1 x 10^6 years
(B) 7.1 x 10^7 years
(C) 7.1 x 10^8 years
(D) 7.1 x 10^9 years
(E) 7.1 x 10^10 years

To be safe the U-235 must be stored for 7.1 * 10^9 years (option D)

Explanation:

Step 1: Data given

Uranium-235 has a half-life of 710 million years.

The radioactivity has dropped to 0.10 percent of the original level.

Step 2: Calculate  how much time must the U-235 be stored securely to be safe?

710 million years = 710000000 years

100 / 2^n = 0.1  

-With 100 = the total % = 100 %

-With n = the half lives = TO BE DETERMINED

-With 0.1 = the % needed to be safe  

100 / 0.1 = 2^n

1000 = 2^n

log 1000 / log 2 = n

n = 9.967  =10

Time needed to store = 710 * 10^6 * 9.967  

Time needed to store = 7.10 * 10^8 * 10

Time needed to store = 7.10 * 10^9 years

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