Question

Use the worked example above to help you solve this problem. The half-life of the radioactive nucleus _(88)^(226)text(Ra) is 1.6 103 yr. If a sample initially contains 4.00 1016 such nuclei, determine the following:________.

(a) the initial activity in curies µCi
(b) the number of radium nuclei remaining after 4.4 103 yr nuclei
(c) the activity at this later time µCi

Answer 1

Step-by-step explanation:

From the information given:

The half-life
`t_(1/2)` = 1.6103 years

The no. of the initial nuclei
`N_o` =
`4.00 * 10^6`

Using the formula:

`N = N_o exp(-\lambda t)`

where;

decay constant
`\lambda = (In2)/(1.6*10^3) y^(-1)`

∴

`N = N_o exp ( (-In2)/(1.6*10^3)* 4.4 * 10^3)`

`N = N_o exp (- 1.906154747)`

The number of radium nuclei N = 5.94 × 10¹⁵

The initial activity
`A_o = \lambda N_o`

`A_o =((In (2))/(1.61* 10^3 * 365 * 24 * 3600)* 4.00 * 10^(16))`

`A_o =546075.8487 \ Bq`

Since;

1 curie = 3.7 × 10¹⁰ Bq

Then;

`A_o =(546075.8487 )/(3.7* 10^(10))`

`A_o = 1.47588 * 10^(-5)Ci`

`A_o = 14.7588 \ \mu Ci`

c) The activity at a later time is:

`=5.94 * 10^(15)( (In (2))/(1.60 * 10^3 * 365* 24 * 3600))`

`= 81599.09018 \ Bq \\ \\ = (81599.09018)/(3.7* 10^(10)) \ Ci \\ \\ = 2.20538 * 10^6 \ Ci \\ \\ = 2.20538 \ \mu Ci`