Question

After 150 days, the activity of a radioactive sample is 5000
dps. The activity becomes 2500 dps after another 75 days.
The initial activity of the sample is
(a) 20000 dps (b) 40000 dps
(c) 7500 dps (d) 10000 dps

Answer 1

After 150 days, the activity of a radioactive sample is 5000 dps. The activity becomes 2500 dps after another 75 days.

To find : let initial activity of the sample is R₀

radioactive is a Frist order reaction.

so use formula, λt = ln [R₀/R]

here t = 150 days then R = 5000 dps

so, λ × 150 = ln [R₀/5000] ......(1)

when t = 150 + 75 = 225 days then R = 2500 dps

λ × 225 = ln [R₀/2500] .......(2)

from equations (1) and (2) we get,

λ × 150/λ × 225 = ln[R₀/5000]/ln[R₀/2500]

⇒2/3 = ln[R₀/5000]/ln[R₀/2500]

⇒2ln[R₀/2500] = 3ln[R₀/5000]

⇒(R₀/2500)² = (R₀/5000)³

⇒R₀²/(2500)² = R₀³/5000³

⇒1/(2500)² = R₀/{(5000)² × (5000)}

⇒1 = R₀/4 × 5000

⇒R₀ = 20,000 dps

Therefore the initial activity of the sample is 20,000 dps.

Answer 2

Answer:

20000 is answer dear friend