Activity of I_131 after 2 days

[soopo]

Homework Statement

The initial activity of I_131 is 0.74MBq.
The half time of I_131 is 8 days.

How large is the activity after two days?

Homework Equations

[tex] A = A_0 e^{-\lambda t} [/tex]

The Attempt at a Solution

We know
t = 2 days
A_0 = 0.74 MBq
T_0.5 = 8 days

1. Solve the activity constant
[tex] \lambda = ln2 / T_0.5 [/tex]

2. Plug it to the equation
[tex] A = A_0 e^{(-ln2 / T_0.5) * t} [/tex]

I standardise the units to SI and then omit/cancel them
[tex] A = 0.74E6 * e^{-ln2 / 4} [/tex]
[tex] = 6.22E5 Bq [/tex]

---

The right answer is 0.4 times what I get
[tex] A = 0.4 * 6.22E5 Bq [/tex]
[tex] = 250 kBq[/tex]

I am not sure where the 0.4 is got.

 

[soopo]

Homework Statement

The initial activity of I_131 is 0.74MBq.
The half time of I_131 is 8 days.

How large is the activity after two days?

Homework Equations

[tex] A = A_0 e^{-\lambda t} [/tex]

The Attempt at a Solution

We know
t = 2 days
A_0 = 0.74 MBq
T_0.5 = 8 days

1. Solve the activity constant
[tex] \lambda = ln2 / T_0.5 [/tex]

2. Plug it to the equation
[tex] A = A_0 e^{(-ln2 / T_0.5) * t} [/tex]

I standardise the units to SI and then omit/cancel them
[tex] A = 0.74E6 * e^{-ln2 / 4} [/tex]
[tex] = 6.22E5 Bq [/tex]

---

The right answer is 0.4 times what I get
[tex] A = 0.4 * 6.22E5 Bq [/tex]
[tex] = 250 kBq[/tex]

I am not sure where the 0.4 is got.

The problem is now solved.

There is the following sentence two pages before the exercise
"Only 40% of the activity in a human is of the form I_131"

 

[nlightner]

The 0.4 is likely the result of rounding or approximation. When using the half-life formula, the actual value after 2 days would be 249.4 kBq, which is approximately 250 kBq. This slight difference may also be due to rounding of the half-life value or the initial activity value. It is important to note that these calculations are based on ideal conditions and may not reflect the exact activity in a real-life scenario. Other factors, such as decay processes and environmental factors, may also affect the activity of I_131. It is always important to consider these factors when interpreting scientific data.