Question

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

Answer 1

Answer:

7.1 × 10⁹ years (D)

Explanation:

half life of the Uranium-235 = 710 million years

to find the time it will take for the U-235 need to be stored securely to be safe

taken the full percent = 100

100 / 2ⁿ = 0.1 where n is number of half-life it has undergone

100 / 0.1 = 2ⁿ

1000 = 2ⁿ

take log of both side

log 1000 / log 2 = n

n = 9.967 number of half-lives

the number of years it will take = 710 million × 9.967 number of half-lives = 7075.7 × 10⁶ years approx 7.1 × 10⁹ years

Answer 2

The correct option is D. $7.1 \times 10^9 years$

• The calculation is as follows:

$100 \div 2^n = 0.1$

here n is number of half-lives it has undergone

$100 \div 0.1 = 2^n\\\\1000 = 2^n$

Now

take log of both side

$log 1000 \div log 2$ = n

n = 9.967 number of half-lives

Now

the number of years it will take should be

$= 710\ million \times 9.967 \\\\= 7075.7 \times 10^6 \\\\= 7.1 \times 10^9 years$

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