Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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The Half-life of 40k is 1.30 × 109 Y. a Sample of 1.00 G of Pure Kci Gives 160 Counts S−1. Calculate the Relative Abundance of 40k (Fraction of 40k Present) in Natural Potassium. - Physics

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Question

The half-life of 40K is 1.30 × 109 y. A sample of 1.00 g of pure KCI gives 160 counts s−1. Calculate the relative abundance of 40K (fraction of 40K present) in natural potassium.

Solution

Given:
Half-life period of 40K,  `T_"1/2"` = 1.30 × 109 years
Count given by 1 g of pure KCI, A = 160 counts/s

Disintegration constant, `lambda = 0.693/T_"1/2"`

Now, activity, A = λN

⇒ `160 = 0.693/t_"1/2" xx N`

⇒ `160 = (0.693/(1.30 xx 10^9 xx 365 xx 86400)) xx N`

⇒ `N = (160 xx 1.30 xx 365 xx 86400 xx 10^9)/0.693`

⇒ `N = 9.5 xx 10^18`

6.023 × 1023 atoms are present in 40 gm.

Thus , `9.5 xx 1018` atoms will be present in `(40 xx 9.5 xx 10^18)/(6.023 xx 10^23)` gm.

= `(4 xx 9.5 xx 10^-4)/6.023` gm

= `6.309 xx 10^-4`

= 0.00063  gm

Relative abundance of 40K  in natural potassium = (2 × 0.00063 × 100)% = 0.12%

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Solution The Half-life of 40k is 1.30 × 109 Y. a Sample of 1.00 G of Pure Kci Gives 160 Counts S−1. Calculate the Relative Abundance of 40k (Fraction of 40k Present) in Natural Potassium. Concept: Radioactivity - Law of Radioactive Decay.
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