Question

After 200 million years, only 1/16 of the original amount of a particular radioactive waste will remain. The half-life of this radioactive waste is how many million years

Answer 1

Answer:

50 millions years

Explanation:

1 to 1/2 to 1/4 to 1/8 to 1/16

It takes 4 half lives to get to 1/16 of the original amount

200 million/4 = 50 millions years

Answer 2

The half-life of the radioactive waste is 50 million years.

To calculate the half-life of the radioactive waste, we use the formula below.

Formula:

• R/R' = $2^{n/a}$............... Equation 1

Where:

• R = Original amount of the radioactive waste
• R' = Remaining amount of the radioactive waste after decay
• n = Total time
• a = Half-life of the radioactive waste.

Assuming: The original amount of the radioactive waste is y

From the question,

Given:

• R = y
• R' = y/16
• n = 200 million years.

Substitute these values into equation 1

• y/(y/16) = $2^{200/a}$
• 16 = $2^{200/a}$

Solve for a

• $2^{200/a}$ = 2⁴

Equating the base

• 200/a = 4
• 4a = 200
• a = 200/4
• a = 50 million years.

Hence, The half-life of the radioactive waste is 50 million years.

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