Chapter 42: Q. 55 (page 1237)

The half-life of the uranium isotope ${}^{235}U$ is $700$ million years. The earth is approximately localid="1650486537957" $4.5$ billion years old. How much more ${}^{235}U$ was there when the earth formed than there is today? Give your answer as the then-to-now ratio.

Short Answer

Expert verified

Then-to-now Ratio of uranium isotope is, $\frac{{(N_{U})}_{0}}{N_{U}} = 86.2$

Step by step solution

Given information

We are given that,

Time is, $t = 4500 m y$

And half life is, $t_{\frac{1}{2}} = 700 m y$

Simplify

Let, amount of uranium isotope when earth is formed is, ${(N_{U})}_{0}$

And amount of uranium isotope now is, $N_{U}$

We know that,

The ${}^{235}U$ decay is given by,

$N_{U} = {(N_{U})}_{0} \times {(\frac{1}{2})}^{\frac{t}{t_{\frac{1}{2}}}}$

Now, ratio is,

localid="1650360018817" $\frac{{(N_{U})}_{0}}{N_{U}} = \frac{1}{{(\frac{1}{2})}^{\frac{t}{t_{\frac{1}{2}}}}} = {(2)}^{\frac{t}{t_{\frac{1}{2}}}} = {(2)}^{\frac{4500 m y}{700 m y}} = 86.2$

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The half-life of the uranium isotope ${}^{235}U$ is $700$ million years. The earth is approximately localid="1650486537957" $4.5$ billion years old. How much more ${}^{235}U$ was there when the earth formed than there is today? Give your answer as the then-to-now ratio.

Short Answer

Step by step solution

Given information

Simplify

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The half-life of the uranium isotope U235is 700million years. The earth is approximately localid="1650486537957" 4.5billion years old. How much more U235was there when the earth formed than there is today? Give your answer as the then-to-now ratio.

Short Answer

Step by step solution

Given information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Engineering Physics

Magnetism and Electromagnetic Induction

Solid State Physics

Astrophysics

Classical Mechanics

Translational Dynamics

Study anywhere. Anytime. Across all devices.

The half-life of the uranium isotope ${}^{235}U$ is $700$ million years. The earth is approximately localid="1650486537957" $4.5$ billion years old. How much more ${}^{235}U$ was there when the earth formed than there is today? Give your answer as the then-to-now ratio.