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Problem 20 Medium Difficulty

Tritium has a half - life of 12.33 years. What fraction of the nuclei in a tritium sample will remain (a) after 5.00 yr? (b) After 10.0 yr? (c) After 123.3 yr? (d) According to Equation 29.4a, an infinite amount of time is required for the entire sample to decay. Discuss whether that is realistic.

Answer

a. 0.755
b. 0.570
c. 9.77 \times 10^{-4}
d. \text { See explanation }

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Top Physics 103 Educators
Elyse G.

Cornell University

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Marshall S.

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Aspen F.

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Video Transcript

number 20. Trillium has 1/2 life of 12.33 years, and we want to know what fraction of a sample remains after five years after 10 years after 123.3 years. Um, I'm gonna use this equation. So this is the original number of nuclei. Um, 1/2 raise to the number of half lives, and that gives you the melt remaining. So if I'm under the fraction, if I would just divide those sides of the equation here by this, the original, that would be the fraction of remains. So I'm basically using I'm solving for this. So the fraction of remaining after five years, it's gonna be 1/2 raised to the five years. I don't know how many half lifes that is. So that'd be five divided by 12.33 So to be less than then 1/2 life. So in your calculator 0.5 raise to the parentheses. E five divided by 12.33 and parentheses. E equals I get 0.755 About 76% is left after five years. After 10 years. So 1/2 raised to the 10 over 12.33 and like it 0.57 So it wasn't a whole half life, so that makes sense. That's still over half of it left. Come on here. 1/2 raised to the 1 23.3 over 12.33 and so on. Until it's 10 half lives, there's still point. 000 977 of the original. I'm late for a party. It says that, um, according to the equation, it would take an infinite amount of time for the entire sample to decay. Is that realistic? You eventually get them to the point where you're left with one and you can't take half of one nuclei and then half of 1/2 and half. So it's going to say that it's not realistic. It would take a long time, but eventually you're down to that last nuclei

University of Virginia
Top Physics 103 Educators
Elyse G.

Cornell University

LB
Liev B.

Numerade Educator

Marshall S.

University of Washington

Aspen F.

University of Sheffield