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

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?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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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