CBSE Class 12 · 2005 · Delhi Compartment · Chemical KineticsShort Answer

During a nuclear explosion, one of the products is

^{90}

Sr with a half-life of 28.1 years. If 1 μg of

^{90}

Sr was absorbed in the bones of a newly born baby instead of calcium, how much of it will remain after 10 years and 60 years if it is not lost metabolically?

Answer: ≈ 0.781 μg after 10 years; ≈ 0.228 μg after 60 years.

Solution

Radioactive decay is first order:

k = \frac{0.693}{t _{1/2}} = \frac{0.693}{28.1} = 0.0247 y r^{- 1}

After 10 years:

lo g \frac{1}{[ R ]} = \frac{k t}{2.303} = \frac{0.0247 \times 10}{2.303} = 0.1071 \Rightarrow [R] = 1 0^{- 0.1071}

[R] = 0.781 μ g

After 60 years:

lo g \frac{1}{[ R ]} = \frac{0.0247 \times 60}{2.303} = 0.6425 \Rightarrow [R] = 1 0^{- 0.6425}

[R] = 0.228 μ g

CBSE Class 12 Board · 2005 · Delhi Compartment · Subjective

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