Calculate Decay Constant of Sodium Isotope: 2.6 Years Half Life

In summary, to find the decay constant of a radioactive isotope with a half life of 2.6 years, convert the time to seconds and use the formula T = (ln2) / λ, where T is the half life in seconds and λ is the decay constant. In this case, the decay constant is 8.4 x 10^-9 s^-1. It is important to remember to convert the time into seconds when using this formula.
  • #1
benhorris
21
0
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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  • #2
[tex] T_h = \frac {ln2} { \lambda} [/tex]



But remember to convert the time into seconds!
 
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  • #3
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.
 
  • #4
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.
 
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FAQ: Calculate Decay Constant of Sodium Isotope: 2.6 Years Half Life

1. What is a decay constant?

A decay constant is a measure of the rate at which a radioactive element decays. It is a constant value that is unique to each radioactive isotope and is used to calculate the amount of time it takes for half of the initial amount of the isotope to decay.

2. How do you calculate the decay constant of a radioactive isotope?

The decay constant of a radioactive isotope can be calculated using the following formula: λ = ln(2) / t1/2, where λ is the decay constant, ln(2) is the natural logarithm of 2, and t1/2 is the half-life of the isotope in question.

3. What is the half-life of the sodium isotope with a decay constant of 2.6 years?

The half-life of a radioactive isotope is the amount of time it takes for half of the initial amount of the isotope to decay. In this case, the half-life of the sodium isotope with a decay constant of 2.6 years is approximately 2.6 years.

4. Can the decay constant of a radioactive isotope change over time?

No, the decay constant of a radioactive isotope is a constant value that does not change over time. It is determined by the properties of the specific isotope and remains the same regardless of the initial amount of the isotope or the amount of time that has passed since its formation.

5. What factors can affect the decay constant of a radioactive isotope?

The decay constant of a radioactive isotope is primarily affected by the properties of the isotope itself, such as its atomic structure and stability. Other factors that can influence the decay constant include temperature, pressure, and the presence of other elements or particles that may interact with the isotope.

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