Question

The half life of uranium-232 is 68.9 years.

a) If you have a 100 gram sample, how much would be left after 250 years?
b) If you have a 100 gram sample, how long would it take for there to be 12.5 grams remaining?

Answer 1

Answer

A) 8.08g

B) 206.7 years

Explanation

Part A)

Formulate the equation:

100g • 0.5^n = mass left

n = number of 68.9 years

250/68.9 = 3.63 ~ (3sf)

substitute n = 3.63

100g • 0.5^3.63 = 8.08g (3sf)

Part B)

100g • 0.5^n = 12.5g

Rearrange to find n

0.5^n = 12.5/100

0.5^n = 0.125

Use logarithms where:

a^c = b log a (b) = c

log 0.5 (0.125) = 3 = n

Since we defined n as number of 68.9 years

3 • 68.9 = 206.7 years

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