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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

\(\mathrm{A}\) and \(\mathrm{B}\) are two radioactive substance whose half lives are 1 and 2 years respectively. Initially \(10 \mathrm{~g}\) of \(\mathrm{A}\) and \(1 \mathrm{~g}\) of \(\mathrm{B}\) is taken. The time after which they will have same quantity remaining is (A) \(3.6\) years (B) 7 years (C) \(6.6\) years (D) 5 years

when \({ }_{3}^{7}\) Li nuclear are bombarded by Proton and the resultant nuclei are \({ }^{8}{ }_{4}\) Be, the emitted particle will be (A) neutron (B) gamma (C) alpha (D) Beta

The hydrogen atom can give spectral lines in the series Lyman, Balmer and Paschen. which of the following statement is correct (A) Lyman series is in the infrared region (B) Balmer series is in the ultraviolet region (C) Balmer series is in the visible region (D) Paschen series is in the visible region.

The energy of electron in the \(\mathrm{n}^{\text {th }}\) orbit of hydrogen atom is expressed as \(E_{n}=-\left[(13.6) / \mathrm{n}^{2}\right] e v .\) The shortest and longest wave length of lyman series will be. (A) \(912 \bar{\AA}, 1216 \AA\) (B) \(1315 \AA, 1530 \AA\) (C) \(5463 \AA, 7858 \AA\) (D) None of these

In Rutherford experiment, the number of Particles scattered at \(90^{\circ}\) angle are 28 Per min. then the number of Particles at the angle \(120^{\circ}\) in Per min will be (A) 25 (B) \(12.0\) (C) 50 (D) 112
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