Question

Assuming the age of the earth to be $10^{10}$ years, what fraction of the original amount of ${ }_{92} \mathrm{U}^{238}$ is still in existence on earth $\left(\mathrm{t}_{1 / 2}\right.$ of ${ }_{92} \mathrm{U}^{238}=4.51 \times 10^{9}$ years $)$ ? (a) $10 \%$ (b) $20 \%$ (c) $30 \%$ (d) $40 \%$

Name: Problem 105, Chapter 21: A Complete Resource Book in Chemistry for JEE Main
Uploaded: 2021-10-08T14:00:28-08:00
Duration: 1 min 37 s
Channel: Narayan Hari
Description: Assuming the age of the earth to be 10^10 years, what fraction of the original amount of 92 U^238 is still in existence on earth (t1 / 2. of 92 U^238=4.51 ×10^9 years ) ? (a) 10 % (b) 20 % (c) 30 % (d) 40 %

   Assuming the age of the earth to be $10^{10}$ years, what fraction of the original amount of ${ }_{92} \mathrm{U}^{238}$ is still in existence on earth $\left(\mathrm{t}_{1 / 2}\right.$ of ${ }_{92} \mathrm{U}^{238}=4.51 \times 10^{9}$ years $)$ ?
(a) $10 \%$
(b) $20 \%$
(c) $30 \%$
(d) $40 \%$

A Complete Resource Book in Chemistry for JEE Main

A.K. Singhal 3rd Edition

Chapter 21, Problem 105

Instant Answer

Solved by Expert Narayan Hari

10/08/2021

Step 1

Step 1: The decay of a radioactive substance is given by the equation $N = N_0 e^{-\lambda t}$, where $N$ is the final amount, $N_0$ is the initial amount, $\lambda$ is the decay constant, and $t$ is the time. Show more…

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Assuming the age of the earth to be $10^{10}$ years, what fraction of the original amount of ${ }_{92} \mathrm{U}^{238}$ is still in existence on earth $\left(\mathrm{t}_{1 / 2}\right.$ of ${ }_{92} \mathrm{U}^{238}=4.51 \times 10^{9}$ years $)$ ? (a) $10 \%$ (b) $20 \%$ (c) $30 \%$ (d) $40 \%$

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Key Concepts

Radioactive Decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. This process occurs spontaneously and follows a probabilistic pattern, resulting in a decrease in the concentration of the radioactive substance over time.

Half-Life

Half-life is the period required for half of the atoms in a sample of a radioactive substance to decay. It is an intrinsic property of each radioactive material and serves as a measure to determine how quickly the substance decays.

Exponential Decay Law

The exponential decay law mathematically models the reduction of radioactive substances over time. By relating the remaining quantity to the time elapsed through an exponential function, it incorporates the decay constant, which is derived from the half-life, enabling precise calculations of the fraction of material remaining after a given period.

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