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Chapter 18: Problem 2537

what Percent of original radioactive substance is left after 5 half life time (A) \(3 \%\) (B) \(5 \%\) (C) \(6 \%\) (D) \(12 \%\)

Short Answer

Expert verified
The remaining percentage of the original radioactive substance after 5 half-lives is approximately \(3\%\), so the correct answer is (A) \(3\%\).

Step by step solution

01

Understand the half-life formula

Half-life (t1/2) is the time it takes for the initial quantity of a radioactive substance to decrease by half. The formula for calculating the remaining quantity after n half-lives have passed is given by: Remaining quantity = Initial quantity * (1/2)^n Where n is the number of half-lives and (1/2)^n is the fraction of the radioactive substance remaining.
02

Apply the formula for the given number of half-lives

In this exercise, we are given that n = 5, which means that 5 half-lives have passed. We will now apply the formula to find the remaining percentage of the initial radioactive substance: Remaining percentage = (1/2)^5
03

Calculate the remaining percentage

To find the remaining percentage, raise 1/2 to the power of 5: Remaining percentage = (1/2)^5 = 1/32 = 0.03125 Now, to convert this fraction into a percentage, we multiply by 100: Remaining percentage = 0.03125 * 100 = 3.125% Since the given answer choices are all integers, we must round this value to the nearest integer. In this case, the closest integer value is 3%.
04

Find the answer

The remaining percentage of the original radioactive substance after 5 half-lives is approximately 3%, so the correct answer is: (A) 3%

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Most popular questions from this chapter

Match column I and II and chose correct Answer form the given below. (a) Nuclear fusion (p) converts some matter into energy (b) Nuclear fission (q) generally Possible for nuclei with low atomic number (c) \(\beta\) decay (r) generally Possible for nuclei with high atomic number (d) Exothermic nuclear (s) Essentially Proceeds by weak reaction nuclear force(c) (A) $\mathrm{a} \rightarrow \mathrm{p}, \mathrm{b} \rightarrow \mathrm{r}, \mathrm{c} \rightarrow \mathrm{s}, \mathrm{d} \rightarrow \mathrm{q}$ (B) $\mathrm{a} \rightarrow \mathrm{q}, \mathrm{b} \rightarrow \mathrm{r}, \mathrm{c} \rightarrow \mathrm{p}, \mathrm{d} \rightarrow \mathrm{s}$ (C) $\mathrm{a} \rightarrow \mathrm{q}, \mathrm{b} \rightarrow \mathrm{r}, \mathrm{c} \rightarrow \mathrm{s}, \mathrm{d} \rightarrow \mathrm{p}$ (D) $\mathrm{a} \rightarrow \mathrm{r}, \mathrm{b} \rightarrow \mathrm{q}, \mathrm{c} \rightarrow \mathrm{p}, \mathrm{d} \rightarrow \mathrm{s}$

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Read the following question and choose correct Answer form given below. (A) Both assertion and reason are true. Reason is the correct explanation of the Assertion. (B) Both assertion and reason are true. Reason is not correct explanation of the assertion. (C) Assertion is true but reason is false. (D) Assertion is false and Reason are true. (i) Assertion :- In a radio-active disintegration, an electron is emitted by nucleus. Reason :- electron are always Present in-side the nucleus. (ii) Assertion :- An electron and Positron can annihilate each other creating Photon Reason:- Electron and Positron form a Particle and anti Particle pair. (iii) Assertion:- An isolated radioactive atom may not decay at all what ever be its half time Reason:- Radioactive decay is a statistical Phenomena. (iv) Assertion:- Fragment Produced in the fission of \(\mathrm{u}^{235}\) are active Reason:- The fragments have abnormally high Proton to neutron ratio
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