Base on this QuestionCan you provide the step in sloving this question? 5. If tp and to are the times required for a radioactive material to decay to 1/p and 1/4 times itsoriginal mass (respectively), how are tp and to related?

Answered: 5. If tp and I are the times required…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 15T

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Can you provide the step in sloving this question?

5. If tp and to are the times required for a radioactive material to decay to 1/p and 1/4 times its
original mass (respectively), how are tp and to related?

Expert Solution

Step 1

Sol:-

The relationship between t_p and t_q can be derived from the general formula for the decay of a radioactive substance, which is:

m = m_o * exp(-λt)

where m is the mass of the radioactive substance at time t, m_o is the initial mass of the substance, λ is the decay constant, and exp(-λt) is the decay factor.

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Suppose that the initial mass of radioactive substance is m0 and the half-life of the substance is h. Let m(t) be the mass remaining at time t. a What is meant by the half-life h? b Write a formula for m(t) in terms of the half-life h. c Write a formula for the relative decay rate r in terms of the half-life h. d Write a formula for m(t) in terms of the relative decay rate r.

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5. If tp and I are the times required for a radioactive material to decay to 1/p and 1/4 times its original mass (respectively), how are tp and to related?