Question

The half life of uranium-232 is 68.9 years. (show step by step)

Answer 1

Answer:

1.) 8.09g ; 2) 206.7 years

Step-by-step explanation:

Given the following :

Half-life(t1/2) of Uranium-232 = 68.9 years

a) If you have a 100 gram sample, how much would be left after 250 years?

Initial quantity (No) = 100g

Time elapsed (t) = 250 years

Find the quantity of substance remaining (N(t))

Recall :

N(t) = No(0.5)^(t/t1/2)

N(250) = 100(0.5)^(250/68.9)

N(250) = 100(0.5)^3.6284470

N(250) = 100 × 0.0808590

= 8.0859045

= 8.09g

2) If you have a 100 gram sample, how long would it take for there to be 12.5 grams remaining?

Using the relation :

N / No = (1/2)^n

Where N = Amount of remaining or left

No = Original quantity

n = number of half-lifes

N = 12.5g ; No = 100g

12.5 / 100 = (1/2)^n

0.125 = (1/2)^n

Converting 0.125 to fraction

(1/8) = 1/2^n

8 = 2^n

2^3 = 2^n

n = 3

Recall ;

Number of half life's (n) = t / t1/2

t = time elapsed ; t1/2 = half life

3 = t / 68.9

t = 3 × 68.9

t = 206.7 years