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Q.54

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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

Consider a nucleus with mass number . Its mass, within , is atomic mass units.

The fact that cancels means that all nuclei have this density. It is a staggeringly large density, roughly times larger than the density of familiar liquids and solids.

One early objection to Rutherford’s model of a nuclear atom was that matter simply couldn’t have a density this high. Although we have no direct experience with such matter, nuclear matter really is this dense.

The expression for the number of atoms present in a sample after some time is .

Here , is the initial number of atoms in the sample, is the time, and is the decay constant.

Therefore, the ratio of calcium atoms to barium atoms after weeks is .

See the step by step solution

Step by Step Solution

Lifetime of  isotope

=

week

Similarly, calculate the lifetime of by substituting for .

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