A radioactive nuclide that is used for radiation therapy for cancer has 33 neutrons and a mass number of 60. Which is the correct symbol for this nuclide?
A. ${}_{80}^{27} Co$
B. ${}_{60}^{33} Co$
C. ${}_{33}^{60} Co$
D. ${}_{27}^{60} Co$
Answer (2)
Determine the number of protons by subtracting the number of neutrons from the mass number: 60 − 33 = 27 .
Identify the element with atomic number 27, which is Cobalt (Co).
Write the symbol for the nuclide in the form Z A X , where A is the mass number and Z is the atomic number.
The correct symbol for the nuclide is 27 60 C o .
Explanation
Understanding the Problem We are given a radioactive nuclide with 33 neutrons and a mass number of 60. We need to find the correct symbol for this nuclide. The general form of a nuclide symbol is Z A X , where A is the mass number, Z is the atomic number (number of protons), and X is the element symbol.
Calculating the Number of Protons First, we need to determine the number of protons in the nuclide. We know that: Mass number (A) = Number of protons (Z) + Number of neutrons (N) So, Number of protons (Z) = Mass number (A) - Number of neutrons (N) In this case, A = 60 and N = 33. Therefore, Z = 60 − 33 = 27
Identifying the Element The number of protons (Z) is 27. This means the atomic number of the element is 27. Looking at the periodic table, the element with atomic number 27 is Cobalt (Co).
Writing the Nuclide Symbol Now we can write the symbol for the nuclide. The mass number (A) is 60, and the atomic number (Z) is 27. So the symbol is 27 60 C o .
Final Answer Comparing this with the given options, we find that the correct symbol is 27 60 C o .
Examples
Radioactive nuclides are used in various fields, including medicine for cancer treatment, industry for gauging thickness, and archaeology for carbon dating. In radiation therapy, a radioactive nuclide like Cobalt-60 ( 27 60 C o ) emits gamma rays that can be directed at cancerous tumors to kill cancer cells. Understanding the properties and symbols of these nuclides is crucial for safe and effective application in these areas. For example, knowing the half-life and decay mode of 27 60 C o helps doctors determine the appropriate dosage and duration of radiation therapy.
The correct symbol for the radioactive nuclide with 33 neutrons and a mass number of 60 is 27 60 C o . This was determined by first calculating the number of protons, which is 27, and identifying the element as Cobalt (Co). Thus, the answer is option D.
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