a.) How much energy is emitted in each alpha decay of plutonium-234 if 234Pu, 234.0433mu and 230U, 230.0338mu.
b.) The half-life of plutonium-234 is 8.8 hrs. How much heat is released by the alpha decay of a 1 micro-gram sample of plutonium-234 in a 24-hour period?
For part a, I understand that you have to use the equation delta E=(delta m)c^2. I'm just not sure if I need to include the mass of the alpha particle when calculating the delta m. I am totally confused on part b. Thanks.
To answer part a of your question, you can use the equation delta E = (delta m) * c^2, as you correctly mentioned. This equation relates the change in energy (delta E) to the change in mass (delta m) and the speed of light (c).
In the case of alpha decay, an alpha particle is emitted. An alpha particle consists of two protons and two neutrons, so its mass is equivalent to the mass of a helium nucleus. The mass of a helium nucleus is approximately 4 atomic mass units (amu).
Now, let's calculate the change in mass (delta m) for the alpha decay of plutonium-234. Plutonium-234 (234Pu) decays into uranium-230 (230U), so we need to calculate the difference in mass between the two isotopes.
The atomic mass of 234Pu is given as 234.0433 amu, and the atomic mass of 230U is given as 230.0338 amu. Therefore, delta m = mass of 234Pu - mass of 230U.
delta m = 234.0433 amu - 230.0338 amu
Now, we can calculate the change in energy (delta E) using the equation delta E = (delta m) * c^2. Make sure to use consistent units, such as electron volts (eV) for energy and grams for mass.
delta E = (delta m) * c^2 = (delta m) * (2.998 x 10^8 m/s)^2
For part b of your question, to calculate the heat released by the alpha decay of a 1 microgram sample of plutonium-234 in a 24-hour period, we need to consider the concept of half-life.
The half-life of a radioactive substance is the time it takes for half of the radioactive nuclei to decay. In this case, the half-life of plutonium-234 is given as 8.8 hours.
To calculate the heat released, we need to consider the decay constant (lambda), which is related to the half-life by the equation:
lambda = ln(2) / half-life
Now, let's calculate the decay constant:
lambda = ln(2) / 8.8 hours
Once you have the decay constant, you can use the exponential decay equation to find the fraction of radioactive nuclei remaining after a certain time. The equation is given by:
N(t) = N(0) * e^(-lambda * t)
Where:
- N(t) is the number of radioactive nuclei remaining at time t,
- N(0) is the initial number of radioactive nuclei,
- lambda is the decay constant,
- t is the time.
Using this equation, you can calculate the fraction of radioactive nuclei remaining after 24 hours (t = 24 hours).
Finally, you can use the mass of plutonium-234 and the fraction of nuclei remaining to calculate the mass remaining after 24 hours. Multiply this mass by the energy change (delta E) calculated in part a to find the total heat released.