Suppose we start with x grams of a sample of radioactive material. y grams of the sample remains

Name: Problem 114, Chapter 5: IIT-JEE Super Course in Mathematics
Uploaded: 2021-09-09T07:38:59-08:00
Duration: 2 min 7 s
Channel: Gaurav Kalra
Description: Suppose we start with x grams of a sample of radioactive material. y grams of the sample remains after a period of n life cycle. The relationship between x and y is given by (a) y=n x+a (b) y=kx 0<k<1 (c) y=(k)/(2) (d) y=(x)/(2^x) where n=0,1,2 ……

step 1 Hi, it is in trying about the half -life of radioactive material. So let's talk in terms of grap

Question

Suppose we start with $\mathrm{x}$ grams of a sample of radioactive material. $\mathrm{y}$ grams of the sample remains after a period of $\mathrm{n}$ life cycle. The relationship between $\mathrm{x}$ and $\mathrm{y}$ is given by (a) $y=n x+a$ (b) $y=\mathrm{kx} 0<\mathrm{k}<1$ (c) $y=\frac{k}{2}$ (d) $y=\frac{x}{2^{x}}$ where $n=0,1,2 \ldots \ldots$

   Suppose we start with $\mathrm{x}$ grams of a sample of radioactive material. $\mathrm{y}$ grams of the sample remains after a period of $\mathrm{n}$ life cycle. The relationship between $\mathrm{x}$ and $\mathrm{y}$ is given by
(a) $y=n x+a$
(b) $y=\mathrm{kx} 0<\mathrm{k}<1$
(c) $y=\frac{k}{2}$
(d) $y=\frac{x}{2^{x}}$ where $n=0,1,2 \ldots \ldots$

IIT-JEE Super Course in Mathematics

Trishna Knowledge… 1st Edition

Chapter 5, Problem 114

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Solved by Expert Gaurav Kalra

09/09/2021

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We start with an initial quantity of the material, which we denote as $x$ grams. Show more…

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Suppose we start with $\mathrm{x}$ grams of a sample of radioactive material. $\mathrm{y}$ grams of the sample remains after a period of $\mathrm{n}$ life cycle. The relationship between $\mathrm{x}$ and $\mathrm{y}$ is given by (a) $y=n x+a$ (b) $y=\mathrm{kx} 0<\mathrm{k}<1$ (c) $y=\frac{k}{2}$ (d) $y=\frac{x}{2^{x}}$ where $n=0,1,2 \ldots \ldots$

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Key Concepts

Decay Factor

The decay factor is a constant between 0 and 1 that represents the proportion of the material remaining after each decay period or life cycle. It is a crucial element in the exponential decay model, as it quantifies the rate at which the material exponentially decreases over time.

Radioactive Decay

Radioactive decay is a process in which unstable atomic nuclei lose energy over time by emitting radiation. This process is characterized by the fact that the loss of material is not linear but follows a predictable pattern, decreasing exponentially as time passes.

Exponential Decay Law

The exponential decay law describes how the quantity of a radioactive substance decreases over time. According to this law, the remaining amount of the substance after a given number of elapsed cycles or time periods is obtained by multiplying the initial amount by a constant decay factor raised to the power of the number of cycles.

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