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The half-life of radium is 1690 years. If 80 grams are present now, how much will be present in 940 years?
56.57 grams
(Do not round until the final answer. Then round to the nearest thoucandth

Ask by Cox Watson. in the United States
Jan 22,2025

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Answer

After 940 years, there will be approximately 54.407 grams of radium present.

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The Deep Dive

To solve the problem, we can use the half-life formula. In 940 years, we can find how many half-lives have passed by dividing 940 by the half-life of radium (1690 years). This gives us approximately 0.555 half-lives.
Now, we can calculate the remaining mass of radium using the formula:
Remaining mass = Initial mass × (1/2)^(number of half-lives).
So, Remaining mass = 80 grams × (1/2)^(0.555). This results in approximately 56.57 grams of radium remaining after 940 years.
In this radioactive decay process, radium slowly transforms into more stable elements, and it’s pretty fascinating to think about how this elemental journey continues far beyond our lifetimes. Each half-life means the amount reduces to half! So, in the grand timeline of 1690 years, radium’s presence continues to dwindle down to mere traces, intricately connected to the atomic world.
You might be surprised to know that radium played a historical role in the glow-in-the-dark paint used for watches and instrument dials! While it made them shine bright, it also caused health problems for the workers who painted with it, leading to critical safety regulations. This serves as a reminder that while science can create wonders, it also brings responsibilities and the need for caution!

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