Inject the gaseous mixture of the three isotopes into a mass spectrometer. This is a machine which determines the composition of different elements in a compound. In this case, this machine is going to determine the percentage abundance of each of the isotopes. You will see lines on the spectrum produced. Basically, how the mass spectrometer works is that the isotopes are ionized to form X+ ions. Then, the ions are accelerated to very high speeds using an electric field. After this, they are passed through a strong magnetic field, which makes the electrically charged ions deviate to go on a curved path. The mass of the ion(in this case, different isotopes have different ions) determines how much it deviates. There is a detector at the end of the machine which detects this, and in turn, the percent composition of different isotopes.
To calculate the atomic weight of an element with multiple isotopes, you multiply the mass of each isotope by its relative abundance (as a decimal), then sum the products. The result is the atomic weight of the element, which is a weighted average of the masses of its isotopes based on their abundance in nature.
The percentage of each isotope is different.
The radioactive isotope is disintegrated in time and emit radiations.
The process in which one isotope changes to another isotope is called radioactive decay. During this process, the unstable nucleus of an isotope emits radiation in the form of alpha particles, beta particles, or gamma rays to transform into a more stable isotope. The rate at which radioactive decay occurs is measured by the isotope's half-life.
The parent isotope is the original radioactive isotope that undergoes decay to form the daughter isotope. The daughter isotope is the stable isotope that is formed as a result of the radioactive decay of the parent isotope.
The percentage of the parent isotope remaining after one half-life of a radioisotope is 50%. This means that half of the parent isotope has decayed into the daughter isotope.
The abundance percentage of each isotope
Because each isotope of an element has a mass different from any other isotope of the same element, and the atomic mass of an element is an average, weighted by the proportion of each isotope, in the naturally occurring element.
Because when they form, minerals in igneous rocks often contain only a parent isotope and none of the daughter isotope. This makes the isotope percentage more accurate and easier to interpret.
Uranium-235 is an isotope of uranium making up about 0.72% of natural uranium.
The precise figure varies from element to element and isotope to isotope depending on the number of neutrons in the nucleus, however it is always at least 99.95% which is the ratio between an electron and a proton.
To find the age of the sample, we need to determine how many half-lives have passed based on the daughter isotope percentage. Since the daughter isotope is 87.5% present, it means 12.5% has decayed from the parent isotope. Since 1 half-life would result in 50% decay, we can divide 12.5% by 50% to get 0.25 half-lives. Therefore, the sample is approximately 150 million years (half-life) x 0.25 = 37.5 million years old.
The basic idea is to measure the amount of the radioactive isotope, and of one or more of its decay products. The older the rock, the larger the percentage of the original isotope that decayed - so the ratio between the original isotope and the decay product changes over time.
Percent abundance is calculated by determining the proportion of a specific isotope of an element relative to the total amount of all isotopes of that element. To find it, divide the number of atoms of the isotope by the total number of atoms of all isotopes, then multiply by 100 to convert it to a percentage. For example, if an element has two isotopes, with 75 atoms of isotope A and 25 atoms of isotope B, the percent abundance of isotope A would be (75 / (75 + 25)) × 100 = 75%.
The stable isotope formed by the breakdown of a radioactive isotope is called a daughter isotope. This process is known as radioactive decay, where a radioactive isotope transforms into a stable daughter isotope through the emission of particles or energy.
The abundance percentage of each isotope
You would need to know the abundance of each isotope to find the average atomic mass of the element. The average atomic mass is calculated by multiplying the mass of each isotope by its relative abundance and then summing these values together.