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The half-life of Cs-137 is 30.2 years. If the initial mass of the sample is 5.00 kg, how much will remain after 90.6 years?

Respuesta :

Answer:

0.625 kg

Explanation:

Since 90.6 is 3 half-lives from 30.2 (90.6/30.2 = 3) , divide the initial mass of the sample by 2, and divide that quotient by 2, and divide THAT quotient by 2 to determine how much remains after 3 half-lives.

The mass will remain at 1.6 kg.

How to find the mass after 90.6 years?

Mass after t years:

The mass of the elements after t years is given by the following equation:

M(t) = M(0)(1-r)[tex]^{t}[/tex]

The half-life of Cs-137 is 30.2 years.

This means that:

M (30.2) = 0.5 M (0)

M (t) = M (0)(0.9773)[tex]^{t}[/tex]

If the initial mass of the sample is 5 kg, how much will remain after 90.6 years?

This is M(151), with M(0) = 100.

Then,

M(90.6) = 5(0.9773)[tex]^{90.6}[/tex]

= 5*0.24

= 1.2 kg

Cesium-137 emits beta particles as it decays to the barium isotope, Ba-137m.

Learn more about initial mass here: brainly.com/question/25573309

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