suppose you had two samples of the same radioactive isotope. one sample had a mass of 25 grams. the other had a mass of 50 grams. would the same number of particles be ejected from each sample in the first hour? explain
No, of course not. The rate that radioactive particles are released is proportional to mass.
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To determine whether the same number of particles would be ejected from each sample in the first hour, we need to understand the concept of radioactive decay and the relationship between mass and the rate of decay.
Radioactive decay is a random process in which unstable atomic nuclei undergo a spontaneous transformation to become more stable. During radioactive decay, particles, such as alpha particles or beta particles, are emitted from the nucleus.
The rate of decay is typically described by the half-life (t½) of an isotope, which is the time it takes for half of the initial sample to decay. Each radioactive isotope has its own specific half-life.
In this case, let's assume that both samples of the radioactive isotope have the same half-life. Now, since we have two samples of the same isotope, it means they have the same decay constant. The decay constant represents the probability of a single atom decaying in a unit of time.
The number of particles ejected from a sample within a given time interval is directly proportional to the number of radioactive atoms in that sample. The more atoms there are, the more particles will be ejected. Thus, a larger mass (or quantity) of the same isotope will contain more atoms, resulting in a greater number of particles being ejected compared to a smaller sample.
Therefore, in the first hour, the sample with a mass of 50 grams would have more particles ejected (assuming the same half-life) compared to the sample with a mass of 25 grams. The exact numerical difference in the number of particles ejected would depend on the specific decay constant and half-life of the isotope involved.
To calculate the exact number of particles ejected from each sample in the first hour, you would need to know the specific decay constant, the half-life of the isotope, and apply the appropriate mathematical equations derived from radioactive decay kinetics.