Technetium-99m is an important isotope used in medical imaging (the m stands for metastable). Each day healthcare professionals around the world use Technetium-99m in thousands of medical scans. This material has a very short half-life of about 6 hours and decays by gamma decay to Technetium-99. In this exercise, you will look at why half-life is an important concern and how it affects your health.
Due to the short half-life of Technetium-99m, this material cannot be easily transported. However, Technetium-99m can be formed from the beta decay of Molybdenum-99, which has a half-life of about 2.75 days. Unfortunately, the world’s supply of molybdenum-99 is in jeopardy as the nuclear facilities that produce this material are beginning to cease operations. Use this information to answer the following questions:
a. Write the nuclear equation for the beta decay of Molybdenum-99.
b. If you have 50 grams of Molybdenum-99, how many grams will remain after 11 days?
c. Would a good solution to the coming shortage of Molybdenum-99 be for hospitals to stockpile large amounts of Molybdenum-99? Why or why not?
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a. The nuclear equation for the beta decay of Molybdenum-99 is:
Mo-99 -> Tc-99 + e-
b. To determine the amount of Mo-99 remaining after 11 days, we need to calculate the number of half-lives that have passed. The half-life of Mo-99 is 2.75 days.
Number of half-lives = time elapsed / half-life
Number of half-lives = 11 days / 2.75 days
Number of half-lives = 4
After 4 half-lives, the amount of Mo-99 remaining can be calculated using the decay formula:
Amount remaining = initial amount * (1/2)^(number of half-lives)
Amount remaining = 50 grams * (1/2)^4
Amount remaining = 50 grams * (1/16)
Amount remaining = 3.125 grams
Therefore, after 11 days, 3.125 grams of Molybdenum-99 will remain.
c. Stockpiling large amounts of Molybdenum-99 may not be a good solution to the coming shortage because of its short half-life. Molybdenum-99 has a half-life of 2.75 days, which means that after a few weeks, the stockpiled material will have decayed significantly, rendering it useless for medical imaging purposes. Additionally, stockpiling large amounts of radioactive material poses safety and security risks. Instead, a better solution would be to find alternative sources for Technetium-99m production or develop new imaging techniques that do not rely heavily on radioactive isotopes.
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