What's the Half-Life for a Sample with Both Gamma and Beta Decay?

In summary, the question asks for the half-life of a sample of radioactive nuclei that can only decay by gamma-emission and beta-emission. After considering the possibility of using the half-life of beta-decay, it is determined that the answer must account for the transformation of the sample into a new nuclear species. The solution involves calculating the decay constant for both types of decay, taking the average, and then converting to half-life.
  • #1
ksac
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Homework Statement



A sample of radioactive nuclei of a certain element
can decay only by gamma -emission and beta -emission. If
the half-life for gamma -emission is 24 minutes and that
for beta -emission is 36 minutes, what's the half-life for the sample?


2. The attempt at a solution

I don't really know how to go about it.

First i thought that may be the half life of the sample should be the half life of beta decay as gamma radiation does not transform the sample into a new element, but only into it's nuclear isomer; but the answer isn't 36 minutes. So clearly it means a new nuclear species by all means.

Then I calculated the decay constant, lambda, for both, took the average and converted the constant to half life.
that still doesn't match the answer given.

How do i do this? :confused:
 
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  • #2
Oh i just realized I shouldn't be averaging the decay constants.
Decay constant = Number of decays per unit time.
So the sum of the two decay constants would give me the total decays in unit time (Gamma or bets).
0.693 times the inverse of that would be my half life.

Forgive me for being too quick to share my confusion. :)
 

FAQ: What's the Half-Life for a Sample with Both Gamma and Beta Decay?

1. What is half life for beta-gamma decay?

Half life for beta-gamma decay is the amount of time it takes for half of the atoms in a sample of a radioactive substance to decay. It is a measure of the stability of a radioactive element, and can be used to predict the rate of decay over time.

2. How is half life for beta-gamma decay calculated?

The half life for beta-gamma decay is calculated by dividing the natural logarithm of 2 by the decay constant, which is a measure of the rate of decay for a particular element. This formula is expressed as t1/2 = ln(2)/λ, where t1/2 is the half life and λ is the decay constant.

3. What factors can affect the half life for beta-gamma decay?

The half life for beta-gamma decay can be affected by several factors, including the type of radioactive element, the environment in which it is located, and any external influences such as temperature or pressure. Additionally, the half life may vary depending on the type of decay (beta or gamma) and the energy of the particles emitted during decay.

4. How does half life for beta-gamma decay relate to radiation exposure?

The half life for beta-gamma decay is important in understanding the level of radiation exposure from a radioactive substance. As the half life decreases, the rate of decay and radiation emitted increases, leading to a higher level of radiation exposure. This is why shorter half lives are associated with more dangerous radioactive materials.

5. Can the half life for beta-gamma decay be changed or manipulated?

The half life for beta-gamma decay is a fundamental property of a radioactive element and cannot be changed or manipulated. It is a natural process that is not affected by external factors. However, scientists can use certain techniques, such as nuclear reactions, to alter the half life of an element and create different isotopes with varying decay rates.

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