A-Level AQA Physics Radioactive Decay: Cobalt-60 has a half-life of 5.2

Cobalt-60 has a half-life of 5.27 years - AQA - A-Level Physics - Question 30 - 2017 - Paper 2

Question 30

Cobalt-60 has a half-life of 5.27 years. What is the total activity of 1.0 g of cobalt-60?

Worked Solution & Example Answer:Cobalt-60 has a half-life of 5.27 years - AQA - A-Level Physics - Question 30 - 2017 - Paper 2

Step 1

Calculate the number of moles in 1.0 g of cobalt-60

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Answer

To find the number of moles, use the formula: $n = rac{m}{M}$ where:

$m$ is the mass of cobalt-60 (1.0 g)
$M$ is the molar mass of cobalt-60 (approximately 60 g/mol)

Thus: $n = \frac{1.0 ext{ g}}{60 ext{ g/mol}} = 0.01667 ext{ moles}$

Step 2

Find the number of radioactive atoms in 1.0 g of cobalt-60

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Answer

Using Avogadro's number ( $N_A = 6.022 imes 10^{23} ext{ atoms/mol}$ ): $N = n \times N_A$ Substituting the values: $N = 0.01667 ext{ moles} \times 6.022 \times 10^{23} ext{ atoms/mol} \approx 1.0 \times 10^{22} ext{ atoms}$

Step 3

Calculate the decay constant ($ frac{ ext{λ}}{ ext{s}}$)

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Answer

The decay constant is calculated using the formula: $ext{λ} = rac{ ext{ln}(2)}{t_{1/2}}$ where $t_{1/2} = 5.27 ext{ years} = 5.27 \times 3.154 \times 10^7 ext{ s}$ . Thus: $ext{λ} = \frac{0.693}{5.27 \times 3.154 \times 10^7} \approx 4.2 \times 10^{-9} ext{ s}^{-1}$

Step 4

Calculate the total activity

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Answer

The activity ( $A$ ) can be calculated with: $A = ext{λ} \times N$ Substituting our values: $A = (4.2 \times 10^{-9} ext{ s}^{-1}) \times (1.0 \times 10^{22} ext{ atoms}) \approx 4.2 \times 10^{13} ext{ Bq}$

Cobalt-60 has a half-life of 5.27 years - AQA - A-Level Physics - Question 30 - 2017 - Paper 2

Worked Solution & Example Answer:Cobalt-60 has a half-life of 5.27 years - AQA - A-Level Physics - Question 30 - 2017 - Paper 2

Calculate the number of moles in 1.0 g of cobalt-60

Find the number of radioactive atoms in 1.0 g of cobalt-60

Calculate the decay constant ($ frac{ ext{λ}}{ ext{s}}$)

Calculate the total activity

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