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Q.46

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 1237

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Short Answer

The activity of a sample of the cesium isotope , with a half-life of 30 years, is . Many years later, after the sample has fully decayed, how many beta particles will have been emitted?

The number of beta particles emitted is .

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Step by Step Solution

Step.1.

Nuclear reaction involves in beta decay of the isotope is given below.

In the each decay, the nucleus decays only one beta particle.

Initial activity of radioactive substance relates with decay rate and initial number of nuclei presented as follows.

Here, is initial activity, is decay rate and is initial number of nuclei.

Rewrite this equation for ,

Step.2.

The relation between decay rate and half-life of a nucleus is,

Here, is half-life.

Substitute for in the equation .

Convert the unit for time from to .

Step.3.

Substitute for and for in the equation , and solve for

Round off to two significant figures,

Therefore, the number of beta particles emitted is .

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