To destroy a cancerous tumor, a dose of gamma radiation totalling an energy of 2.12J is to be delivered in 30 days from implanted sealed capsule containing palladium -103. Assuming that this isotope has half life of 17 days and emits gamma rays of radiation 21.0 Kev, which are entirely absorbed within the tumor. What is the initial activity of the set of capsules and what total mass of the radioactive palladium should these seeds contain?
Radioactive decay
The emission of energy to produce ionizing radiation is known as radioactive decay. Alpha, beta particles, and gamma rays are examples of ionizing radiation that could be released. Radioactive decay happens in radionuclides, which are imbalanced atoms. This periodic table's elements come in a variety of shapes and sizes. Several of these kinds are stable like nitrogen-14, hydrogen-2, and potassium-40, whereas others are not like uranium-238. In nature, one of the most stable phases of an element is usually the most prevalent. Every element, meanwhile, has an unstable state. Unstable variants are radioactive and release ionizing radiation. Certain elements, including uranium, have no stable forms and are constantly radioactive. Radionuclides are elements that release ionizing radiation.
Artificial Radioactivity
The radioactivity can be simply referred to as particle emission from nuclei due to the nuclear instability. There are different types of radiation such as alpha, beta and gamma radiation. Along with these there are different types of decay as well.
To destroy a cancerous tumor, a dose of gamma
The formula for the decay constant is:
The formula for the number of nuclei remains after t days is:
Therefore, the number of nuclei undergoes decay is:
As mentioned in the question, the decayed nuclei released a total of 2.12 J radiation. Thus,
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