The half life of silicon 32 is 710 years

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Question:

The half-life of silicon-32 is 710 years. If 30 grams are present now, how much will be present in 300 years?

Exponential Decay based Problem:

The amount of radioactive material {eq}N {/eq} compared to the original amount {eq}N_0 {/eq} or any quantity which is proportional to {eq}N {/eq}. The longer the half-life, the lower the decay constant as they are inversely proportional to each other.

Answer and Explanation: 1

{eq}{/eq}

Given that

Initial Amount {eq}N_0 = 30 {/eq} grams

Half-life period {eq}t = 710 {/eq} years

Time to decay {eq}t_0 = 300 {/eq} years

The radioactive decay formula is given by

$$\begin{align} \displaystyle N &= N_0 \times 2^{\frac{-t_0}{t}}\\ \displaystyle N &= 30 \times 2^{\frac{-100}{710}}\\ \displaystyle N &= 30 \times 2^{-0.1408}\\ \displaystyle N &= 30 \times 2^{-0.1408}\\ N &\approx 27.2104 \ grams \end{align} $$

Therefore, the amount of Silicon present after {eq}300 {/eq} years will be {eq}27.2104 {/eq} grams

Learn more about this topic:

Exponential Decay: Examples & Definition

from

Chapter 5 / Lesson 7

In this lesson, learn about exponential decay and find real-life exponential decay examples. Learn how to use the model to solve exponential decay example problems.

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