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During nuclear explosion, one of the products is 90Sr with half-life of 28.1 years. If 1μg of 90Sr 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. - Chemistry

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Question

During nuclear explosion, one of the products is 90Sr with half-life of 28.1 years. If 1μg of 90Sr 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.

Solution

Here, k = `0.693/t_"1/2" = 0.693/28.1 y^(-1)`

It is known that,

`t = 2.303/k log  ([R]_0)/([R])`

`=> 10 = 2.303/(0.693/28.1) log  1/[R]`

`=>10 = 2.303/(0693/28.1)(-log [R])`

`=> log [R] = -(10xx0.693)/(2.303xx28.1)`

=>[R] = antilog (-0.1071)

= antilog(`(bar"1".8929`)

= 0.7814 `mug`

Therefore, 0.7814 μg of 90Sr will remain after 10 years.

Again,

` t= 2.303/k log  ([R]_0)/([R])`

`=> 60 = 2.303/(0.693/28.1) log  1/[R]`

`=>log[R] = -(60xx0.693)/(2.303xx28.1)`

=>[R] = antilog (-0.6425)

=antilog(`bar"1"`.3575)

= 0.2278 `mug`

Therefore, 0.2278 μg of 90Sr will remain after 60 years

  Is there an error in this question or solution?
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APPEARS IN

 NCERT Solution for Chemistry Textbook for Class 12 (2018 (Latest))
Chapter 4: Chemical Kinetics
Q: 17 | Page no. 119
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During nuclear explosion, one of the products is 90Sr with half-life of 28.1 years. If 1μg of 90Sr 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. Concept: Integrated Rate Equations - Half-life of a Reaction.
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