Calculate Decay Constant of Sodium Isotope: 2.6 Years Half Life

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Homework Help Overview

The discussion revolves around calculating the decay constant of a sodium isotope given its half-life of 2.6 years. The subject area pertains to radioactive decay and the mathematical relationships involved in determining decay constants.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the formula relating half-life to decay constant, specifically T_h = ln(2) / λ. There are questions about the necessary unit conversions from years to seconds.

Discussion Status

Some participants have provided guidance on the conversion process needed to apply the formula correctly. There is acknowledgment of a mistake made in the conversion, but no consensus on a final resolution has been reached.

Contextual Notes

Participants are working under the constraint of converting time from years to seconds, which is critical for the calculation. There is an emphasis on ensuring all units are correctly accounted for in the process.

benhorris
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Simple question, but i don't know where to start.

The half life of one radioactive isotope of sodium is 2.6 years. Show that its decay constant is 8.4 x 10^-9 s^-1.

Thanks in advance,

Ben.
 
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[tex]T_h = \frac {ln2} { \lambda}[/tex]



But remember to convert the time into seconds!
 
Last edited:
Do you know the following identity [itex]T = \frac{ln 2}{\lambda}[/itex], where [itex]T[/itex] is the half life in seconds and [itex]\lambda[/itex] is the decay constant.
 
Ah got it,

Thanks guys.

Was a simple error, i converted it to seconds by doing =

2.6 x 365 x 3600. And i forgot about the hours.

3600 x 24 x 365 x 2.6 = no.seconds gave the correct answer.

Silly mistake.
 
Last edited:

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