/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 3 The probability of a radioactive... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 19: Problem 3

The probability of a radioactive atom for not disintegrating till 3 times of its half-life is (A) \(\frac{1}{3}\) (b) \(\frac{1}{4}\) (C) \(\frac{1}{8}\) (D) \(\frac{7}{8}\)

Short Answer

Expert verified
The probability of a radioactive atom not disintegrating till 3 times of its half-life is \(\frac{1}{8}\), corresponding to option (C).

Step by step solution

01

Write down the formula for remaining atoms after a certain number of half-lives

Use the formula \(N_t = N_0 (1/2)^n\) for this problem.
02

Find the number of half-lives

The problem states that we must find the probability of a radioactive atom not disintegrating till 3 times of its half-life, so in this case, n=3.
03

Rewrite the formula given n

Since n=3, the formula we have is \(N_t = N_0 (1/2)^3\).
04

Determine the probability

Since we want to find the probability of an atom not disintegrating till 3 times of its half-life, we just need to calculate the fraction of the original number of atoms which remain after 3 half-lives have passed. Hence, divide the remaining atoms (\(N_t\)) by the original number of atoms (\(N_0\)): \(P = \frac{N_t}{N_0} = \frac{N_0 (1/2)^3}{N_0}\)
05

Simplify the probability expression

As \(N_0\) is on both numerator and denominator, they cancel each other out. Therefore, the probability expression becomes: \(P = (1/2)^3\).
06

Calculate the probability

Now, evaluate the expression to find the probability: \(P = (1/2)^3 = \frac{1}{8}\). Hence, the probability of a radioactive atom not disintegrating till 3 times of its half-life is \(\frac{1}{8}\), which corresponds to option (C).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The energy that should be added to an electron, to reduce its de-Broglie wavelengths from \(10^{-10} \mathrm{~m}\) to \(0.5 \times 10^{-10} \mathrm{~m}\), will be (A) four times the initial energy. (B) thrice the initial energy. (C) equal to the initial energy. (D) twice the initial energy.

Starting with a sample of pure \({ }^{66} \mathrm{Cu}, \frac{7}{8}\) of it decays into \(\mathrm{Zn}\) in 15 minutes. The corresponding half-life is (A) \(15 \mathrm{~min}\) (B) \(10 \mathrm{~min}\) (C) \(7 \frac{1}{2} \mathrm{~min}\) (D) \(5 \mathrm{~min}\)

This question contains Statement 1 and statement \(2 .\) Of the four choices given after the statements, choose the one that best describes the two statements. [2008] Statement 1: Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion and Statement 2: For heavy nuclei, binding energy per nucleon increases with increasing \(Z\) while for light nuclei it decreases with increasing \(Z\). (A) Statement 1 is true, Statement 2 is false (B) Statement 1 is false, Statement 2 is true (C) Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for statement 1 (D) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1

Which of the following statement about \(x\)-rays is/are true? (A) \(E\left(K_{\alpha}\right)+E\left(L_{\beta}\right)=E\left(K_{\beta}\right)+E\left(M_{\alpha}\right)=E\left(K_{\gamma}\right)\), where \(E\) is the energy of respective \(x\)-rays. (B) For the harder \(x\)-rays, the intensity is higher than soft \(x\)-rays. (C) The continuous and the characteristic \(x\)-rays differ only in the method of creation. (D) The cut-off wavelength \(\lambda_{\min }\) depends only on the accelerating voltage applied between the target and the filament.

Which of the following transitions in hydrogen atoms emit photons of highest frequency? (A) \(n=1\) to \(n=2\) (B) \(n=2\) to \(n=6\) (C) \(n=6\) to \(n=2\) (D) \(n=2\) to \(n=1\)
See all solutions

Recommended explanations on Physics Textbooks

Energy Physics

Read Explanation

Solid State Physics

Read Explanation

Electricity

Read Explanation

Waves Physics

Read Explanation

Kinematics Physics

Read Explanation

Fields in Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.