Half Life / Alpha Decay Question - No IDea

In summary, the question is about the age of a space rock that contains 3.20 g of 147Sm and 0.110 g of 143Nd, with a half-life of 1.06x10^11 years. The solution involves using the decay formula and assuming that all the mass was samarium to determine the age of the rock.
  • #1
wayneinsane
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Half Life / Alpha Decay Question -- No IDea

Homework Statement



A space rock contains 3.20 g of 147 62 Sm and 0.110 g of 143 60 Nd. 147 62 Sm alpha decays to 143 60 Nd with a half-life of 1.06 1011 yr. If the rock originally contained no , how old is it?

Homework Equations



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The Attempt at a Solution



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  • #2


If you presume that it was all samarium with no neodymium, then all you need to do is apply the decay formula to the original sample as though all the mass was samarium. (Now it's true that the alpha particles emitted represent a loss of mass, but I'd think since the neodymium is a minor fraction of the samarium you can ignore the loss.)
 
  • #3


I would first like to clarify the question and gather more information. It is important to know the specific isotope of 147Sm and 143Nd, as well as their respective atomic masses, in order to accurately calculate the mass difference and determine the amount of decay that has occurred.

Additionally, it would be helpful to know the initial amount of 147Sm in the rock, as well as the current amount of 147Sm and 143Nd, in order to determine the amount of decay that has taken place.

Once all of this information is gathered, I would use the equation for half-life to calculate the age of the rock. The equation is t = (ln 2)/λ, where t is the age of the sample, ln 2 is the natural logarithm of 2, and λ is the decay constant. The decay constant can be calculated using the half-life and the initial and final amounts of the decaying isotope.

In conclusion, without more information and calculations, it is not possible to accurately determine the age of the rock. Gathering more data and using the appropriate equations will allow for a more precise and scientific answer.
 

What is half-life?

Half-life is the amount of time it takes for a radioactive substance to decay by half. This means that if you start with 100 atoms of a radioactive substance, after one half-life, there will be 50 atoms remaining.

How is half-life measured?

Half-life is measured by the rate of decay of a radioactive substance. This is usually done by counting the number of atoms that decay over a certain period of time and then calculating the time it takes for half of the atoms to decay.

What is the relationship between half-life and radioactive decay?

Half-life and radioactive decay are directly related. The shorter the half-life, the faster the rate of decay. This means that a substance with a short half-life will decay faster than a substance with a longer half-life.

What is alpha decay?

Alpha decay is a type of radioactive decay where an unstable atom releases an alpha particle, which consists of two protons and two neutrons. This process results in the atom transforming into a different element with a lower atomic number.

How does alpha decay occur?

Alpha decay occurs when an atom has too many protons and neutrons in its nucleus, making it unstable. To become more stable, the atom releases an alpha particle, which reduces the number of protons and neutrons in the nucleus, creating a new element.

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