Half-life is the period of time it takes for the amount of a radioactive substance to decrease by half. Carbon-14 has a half-life of 5730 years. As observed from Earth, what would the half-life of carbon-14 be if it travelled through space at 25% of the speed of light, relative to Earth?

Half-life is the period of time it takes for the amount of a radioactive substance to decrease by half. Carbon-14 has a half-life of 5730 years. As observed from Earth, what would the half-life of carbon-14 be if it travelled through space at 25% of the speed of light, relative to Earth?

Astronomy

1st Edition

ISBN:9781938168284

Author:Andrew Fraknoi; David Morrison; Sidney C. Wolff

Publisher:Andrew Fraknoi; David Morrison; Sidney C. Wolff

Chapter16: The Sun: A Nuclear Powerhouse

Section: Chapter Questions

Problem 31E: The Sun converts 4109 kg of mass to energy every second. How many years would it take the Sun to...

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Question

Definition Definition Rate at which light travels, measured in a vacuum. The speed of light is a universal physical constant used in many areas of physics, most commonly denoted by the letter c . The value of the speed of light c = 299,792,458 m/s, but for most of the calculations, the value of the speed of light is approximated as c = 3 x 10 8 m/s.

Expert Solution

Step 1

The time dilation equation is,

$τ = \frac{τ_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$

Here, the total life is $τ_{0}$ ,

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