To solve this problem, we need to use the formula for radioactive decay, which is:

Activity (A) = (No of atoms) * (decay constant)

The decay constant (λ) is related to the half-life (T) of the substance by the formula:

λ = 0.693 / T

First, we need to find the number of atoms in the 2.7mg sample of Indium-116. We know that 1 mole of Indium-116 has a mass of 116g (from the periodic table), and contains Avogadro's number (6.022 x 10^23) of atoms.

So, the number of atoms in 2.7mg (or 0.0027g) of Indium-116 is:

No of atoms = (0.0027/116) * 6.022 x 10^23 = 1.40 x 10^20 atoms

Next, we calculate the decay constant using the given half-life of 14.10 seconds:

λ = 0.693 / 14.10 = 0.0492 s^-1

Now we can calculate the activity:

A = (1.40 x 10^20 atoms) * (0.0492 s^-1) = 6.89 x 10^18 Bq

To convert this to curies, we use the conversion factor 1 Ci = 3.7 x 10^10 Bq:

A = (6.89 x 10^18 Bq) / (3.7 x 10^10 Bq/Ci) = 1.86 x 10^8 Ci

So, the activity of the 2.7mg sample of Indium-116 is 6.89 x 10^18 Bq or 1.86 x 10^8 Ci.

Question

To solve this problem, we need to use the formula for radioactive decay, which is:

Activity (A) = (No of atoms) * (decay constant)

The decay constant (λ) is related to the half-life (T) of the substance by the formula:

λ = 0.693 / T

First, we need to find the number of atoms in the 2.7mg sample of Indium-116. We know that 1 mole of Indium-116 has a mass of 116g (from the periodic table), and contains Avogadro's number (6.022 x 10^23) of atoms.

So, the number of atoms in 2.7mg (or 0.0027g) of Indium-116 is:

No of atoms = (0.0027/116) * 6.022 x 10^23 = 1.40 x 10^20 atoms

Next, we calculate the decay constant using the given half-life of 14.10 seconds:

λ = 0.693 / 14.10 = 0.0492 s^-1

Now we can calculate the activity:

A = (1.40 x 10^20 atoms) * (0.0492 s^-1) = 6.89 x 10^18 Bq

To convert this to curies, we use the conversion factor 1 Ci = 3.7 x 10^10 Bq:

A = (6.89 x 10^18 Bq) / (3.7 x 10^10 Bq/Ci) = 1.86 x 10^8 Ci

So, the activity of the 2.7mg sample of Indium-116 is 6.89 x 10^18 Bq or 1.86 x 10^8 Ci.

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