The half-life for U 238 is 4.5x109 years. a) If five half-lives have gone by how many years have gone by?
b) If you start with 240 grams of U 238 and end up with 60 grams, how many years have gone by?
c) If you start with 240 grams of U 238 and 1.8 x 10^10 years go by, how much U 238 is left?
d) If you start with 562 g and six half lives go by how many grams are left?

a. 2.25 × 10^10 yrs

b. 9 × 10^9 yrs

c. 59.5g

d. 8.78g

Explanation:

(a) Original sample(N) = 238g

Half-life = 4.5 × 10^9 yrs

5 half-life 5T½ = 5 × 4.5 × 10^9 yrs

= 2.25 × 10^10 yrs

(b) If N = 240g

N/2 = 120g

N/4 = 60g

Meaning 2T½

= 2 × 4.5 × 10^9 yrs

= 9 × 10^9 yrs

(c) 1.8 × 10^10 ÷ 4.5 × 10^9 = 4

at 4T½ we have N/16 = 238/4 = 59.5

=> the sample left = 59.5g

(d) from the question N = 562g

at 6T½

the amount left will be N/64

= 562÷64 = 8.78g

NB: For questions please you can read more on radioactivity

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