Obtain the amount of 60Co necessary to provide source of 8.0Ci strength .The half life of 60Co is 5.3 years.

To determine the amount of cobalt-60 (60Co) needed to achieve a source strength of 8.0 curies (Ci), we first need to understand the relationship between the activity of a radioactive substance, its half-life, and the amount of the substance present. Let's break this down step by step.

Understanding Radioactive Decay

Radioactive decay is a process where unstable atomic nuclei lose energy by emitting radiation. The activity of a radioactive source, measured in curies, indicates how many disintegrations occur per second. One curie is defined as 3.7 x 10¹⁰ disintegrations per second.

Activity and Amount Relationship

The activity (A) of a radioactive substance can be calculated using the formula:

• A = λN

Where:

• A = activity in disintegrations per second (Bq)
• λ = decay constant (in s^-1)
• N = number of radioactive atoms present

Calculating the Decay Constant

The decay constant (λ) is related to the half-life (T_1/2) of the substance by the formula:

• λ = ln(2) / T_1/2

For cobalt-60, the half-life is given as 5.3 years. First, we need to convert this into seconds:

• 5.3 years = 5.3 x 365.25 days/year x 24 hours/day x 3600 seconds/hour
• 5.3 years ≈ 1.67 x 10⁸ seconds

Now, we can calculate λ:

• λ = ln(2) / (1.67 x 10⁸ s) ≈ 4.14 x 10^-9 s^-1

Finding the Required Number of Atoms

Next, we need to convert the desired activity of 8.0 Ci into disintegrations per second:

• 8.0 Ci = 8.0 x 3.7 x 10¹⁰ Bq ≈ 2.96 x 10¹¹ Bq

Now, we can rearrange the activity formula to find N:

• N = A / λ
• N = (2.96 x 10¹¹ Bq) / (4.14 x 10^-9 s^-1) ≈ 7.15 x 10¹⁹ atoms

Calculating the Mass of Cobalt-60

To find the mass of cobalt-60 required, we need to know the number of atoms in a mole (Avogadro's number, approximately 6.022 x 10²³ atoms/mole) and the molar mass of cobalt-60 (approximately 59.933 g/mol):

• Mass = (N / Avogadro's number) x Molar mass
• Mass = (7.15 x 10¹⁹ atoms / 6.022 x 10²³ atoms/mole) x 59.933 g/mol
• Mass ≈ 0.071 g

Final Result

To achieve a source strength of 8.0 Ci, you would need approximately 0.071 grams of cobalt-60. This calculation illustrates the relationship between the half-life, activity, and amount of radioactive material, providing a clear understanding of how to work with radioactive isotopes in practical applications.