Question

The beta decay of cesium-137 has a half-life of 30.0 years. How many years must pass to
reduce a 25 mg sample of cesium-137 to 8.7 mg?
meg.


A 46 B. 32 C. 32 D. 52​

Answer 1

Answer:

46

Explanation:

Answer 2

Given: the half-life of beta decay of cesium-137, t = 30.0 years

           the initial concentration of cesium-137, N₀ = 25 mg

           the final concentration of cesium-137, Nₓ = 8.7 mg

To Find: the time taken by cesium-137 to get reduced, T.

Solution:

To calculate T, the formula used:

• ln ( Nₓ / N₀)  =  - k x T                            ⇒ 1
• k = 0.693 / t
• here, k is the rate constant

Applying the above formula :

k = 0.693 / 30

  = 0.023

Putting the value of k in equation 1 :

ln (8.7 / 25) = - 0.023 x T

In (0.35)      = - 0.023 x T

- 1.04 = - 0.023 x T

Cancelling negative sign on both the side:

0.023 x T = 1.04

T = 1.04 / 0.023

  = 45.2

T = 45.2 years.