   Chapter 31, Problem 12PE

Chapter
Section
Textbook Problem

If a 1.50−cm−thick piece of lead can absorb 90.0% of the γ rays from a radioactive source, how many centimeters of lead are needed to absorb all but 0.100% of the γ rays?

To determine

The thickness of lead in centimeters needed to absorb all but 0.100% of γ rays.

Explanation

Given info:

The thickness of lead that can absorb 90.0% of γ rays

x=1.50 cm

Formula used:

The fraction f of γ rays that remain unabsorbed is given by,

f=eμx

Here, µ is the absorption coefficient of lead.

Calculation:

The 1.50 cm thick lead can absorb 90.0% of γ rays. Therefore, the fraction that remains is 10.0%.

Substitute 10.0100 for f and 1.50 cm for x to calculate the value of µ.

f=eμx10.0100=eμ1.50 cmeμ1.50 cm=0.100μ1.50 cm=ln10μ=1

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