Suppose you had two samples of the same radioactive isotope one that weighs 25g and one that weighs 50g would the same number of particles be ejected from each sample in the first hour,explain.
To determine whether the same number of particles will be ejected from each sample in the first hour, we need to understand the concept of radioactive decay.
Radioactive decay is a random process in which unstable atomic nuclei lose energy by emitting radiation. This emission can occur as alpha particles, beta particles, or gamma rays. The rate of decay is measured in terms of the half-life, which is the time it takes for half of the radioactive sample to decay.
In this scenario, we have two samples of the same radioactive isotope, one weighing 25g and the other weighing 50g. The weight of the samples alone does not directly affect the rate of decay. Instead, decay is determined by the number of radioactive atoms present.
The number of radioactive atoms in a sample is directly proportional to its weight and the Avogadro's number, which is approximately 6.022 x 10^23. Avogadro's number represents the number of particles per mole of a substance.
To determine the number of particles in each sample, we need to use the molar mass of the isotope. Let's assume the molar mass of the isotope is M g/mol.
For the 25g sample:
Number of particles = (25g / M g/mol) x (6.022 x 10^23 particles/mol)
For the 50g sample:
Number of particles = (50g / M g/mol) x (6.022 x 10^23 particles/mol)
So, if the molar mass is the same for both samples, the 50g sample will have twice the number of particles compared to the 25g sample, assuming all other factors remain the same.
Therefore, in the first hour, you would expect the 50g sample to eject approximately twice the number of particles compared to the 25g sample.