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Chapter 18: Problem 2521

A freshly Prepared radioactive source of half life \(2 \mathrm{~h}\) emits radiation of intensity which is 64 times the Permissible safe level. The minimum time after which is would be possible to work safely with this source is. (A) \(6 \mathrm{~h}\) (B) \(24 \mathrm{~h}\) (C) \(12 \mathrm{~h}\) (D) \(36 \mathrm{~h}\)

Short Answer

Expert verified
The minimum time after which it would be possible to work safely with this source is 12 hours. So, the correct answer is (C) 12 hours.

Step by step solution

01

Determine number of half-lives required to reach safe level

First, we need to figure out how many times the source must go through its half-life to reduce its intensity to the safe level. The source emits radiation at 64 times the safe level, so we'll need to find the smallest number of half-lives that will multiply by a factor of 1/2 to reduce the intensity to 1 or below.
02

Calculate the number of half-lives

Starting with the source at 64 times the safe level, consider going through the half-lives: 1st half-life: \(64\cdot\frac{1}{2}=32\) times the safe level. 2nd half-life: \(32\cdot\frac{1}{2}=16\) times the safe level. 3rd half-life: \(16\cdot\frac{1}{2}=8\) times the safe level. 4th half-life: \(8\cdot\frac{1}{2}=4\) times the safe level. 5th half-life: \(4\cdot\frac{1}{2}=2\) times the safe level. 6th half-life: \(2\cdot\frac{1}{2}=1\) time the safe level (finally within the safe level). Thus, the source must go through 6 half-lives to reach the safe level.
03

Calculate the minimum time for safe work

Now that we know the number of half-lives, we can calculate the time required to reach the safe level. Each half-life is 2 hours long, and this process will take 6 half-lives. Therefore, the total time required to reach the safe level is: Minimum time = Number of half-lives × Half-life time duration Minimum time = 6 × 2 hours = 12 hours The minimum time after which it would be possible to work safely with this source is 12 hours. So, the correct answer is (C) 12 hours.

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Most popular questions from this chapter

The innermost orbit of the hydrogen atom has a radius \(0.53 \mathrm{~A}\). what is radius of \(2^{\text {nd }}\) orbit is ? (A) \(2.12 \AA\) (B) \(1.06 \AA\) (C) \(21.2 \AA\) (D) \(10.6 \AA\)

two deuterons each of mass \(\mathrm{m}\) fuse to form helium resulting in release of energy \(\mathrm{E}\) the mass of helium formed is (A) \(\mathrm{m}+\left(\mathrm{E} / \mathrm{C}^{2}\right)\) (B) \(\left[\mathrm{E} /\left(\mathrm{mC}^{2}\right)\right]\) (C) \(2 \mathrm{~m}-\left(\mathrm{E} / \mathrm{C}^{2}\right)\) (D) \(2 \mathrm{~m}+\left(\mathrm{E} / \mathrm{C}^{2}\right)\)

Nucleon is common name for (A) electron and neutron (B) proton and neutron (C) neutron and positron (D) neutron and neutrino

which of the following cannot be emitted in radioactive decay of the substance? (A) Helium-nucleus (B) Electrons (C) Neutrinos (D) Proton.

starting with a sample of Pure \({ }^{66} \mathrm{cu},(7 / 8)\) of it decays into \(\mathrm{Zn}\), 15 minutes. The half life the sample is (A) \(5 \mathrm{~min}\) (B) \(7.5 \mathrm{~min}\) (C) \(10 \mathrm{~min}\) (D) \(15 \mathrm{~min}\)
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