Stop speaking French to me 😡😡😡😡redo question 6 in English

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2 parts
b(i)

4 days4 \text{ days}

b(ii)

4.7×102 Bq4.7 \times 10^2 \text{ Bq}

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I apologize for the language mix-up. Here is Question 6 re-done in English:

Part 6

a) The half-life (T1/2T_{1/2}) of a radioactive isotope is the time required for half of the radioactive nuclei in a sample to decay. It is also the time required for the activity of a radioactive sample to be reduced by half.

Part b(i)

4 days4 \text{ days}

To determine the half-life of the isotope

  1. Use the radioactive decay formula A=A0(12)nA = A_0 \left(\frac{1}{2}\right)^n, where nn is the number of half-lives.

    Initial activity $A_0 = 1.2 \times 10^5 \text{ Bq}$.  
    Activity after $t = 12 \text{ days}$ is $A = 1.5 \times 10^4 \text{ Bq}$.
    $$
    \frac{A}{A_0} = \left(\frac{1}{2}\right)^n
    $$
    $$
    \frac{1.5 \times 10^4 \text{ Bq}}{1.2 \times 10^5 \text{ Bq}} = \left(\frac{1}{2}\right)^n
    $$
    $$
    0.125 = \left(\frac{1}{2}\right)^n
    $$
    
  2. Solve for nn.

    We know that $0.125 = \frac{1}{8} = \left(\frac{1}{2}\right)^3$.  
    Therefore, $n = 3$.
    
  3. Calculate the half-life T1/2T_{1/2} using n=tT1/2n = \frac{t}{T_{1/2}}.

    $$
    3 = \frac{12 \text{ days}}{T_{1/2}}
    $$
    $$
    T_{1/2} = \frac{12 \text{ days}}{3}
    $$
    $$
    T_{1/2} = 4 \text{ days}
    $$
    The half-life of the isotope is $\boxed{4 \text{ days}}$.
    

Part b(ii)

4.7×102 Bq4.7 \times 10^2 \text{ Bq}

To calculate the activity of the sample after an additional 20 days

  1. Calculate the total time elapsed.

    Total time $t_{\text{total}} = 12 \text{ days} + 20 \text{ days} = 32 \text{ days}$.
    
  2. Calculate the total number of half-lives n′n' for this time.

    $$
    n' = \frac{t_{\text{total}}}{T_{1/2}} = \frac{32 \text{ days}}{4 \text{ days}}
    $$
    $$
    n' = 8
    $$
    
  3. Calculate the final activity A′A'.

    $$
    A' = A_0 \left(\frac{1}{2}\right)^{n'}
    $$
    $$
    A' = (1.2 \times 10^5 \text{ Bq}) \times \left(\frac{1}{2}\right)^8
    $$
    $$
    A' = (1.2 \times 10^5 \text{ Bq}) \times \frac{1}{256}
    $$
    $$
    A' \approx 468.75 \text{ Bq}
    $$
    $$
    A' \approx 4.7 \times 10^2 \text{ Bq}
    $$
    The activity of the sample after an additional 20 days will be approximately $\boxed{4.7 \times 10^2 \text{ Bq}}$.
    
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