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The half-life of a radioisotope is six hours. If the initial mass of the isotope is 200 g, then the mass (in g) remaining after 24 hours undecayed will be (Nearest integer)
Correct answer is '13'. Can you explain this answer?
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The half-life of a radioisotope is six hours. If the initial mass of ...
Understanding Half-Life
The half-life of a radioisotope is the time required for half of the isotope to decay. In this case, the half-life is 6 hours.
Calculation of Remaining Mass
To find the remaining mass after 24 hours, follow these steps:
1. Determine the Number of Half-Lives:
- Total time = 24 hours
- Half-life = 6 hours
- Number of half-lives = Total time / Half-life = 24 hours / 6 hours = 4
2. Calculate Remaining Mass:
- Initial mass = 200 g
- After each half-life, the mass is halved:
- After 1st half-life (6 hours): 200 g / 2 = 100 g
- After 2nd half-life (12 hours): 100 g / 2 = 50 g
- After 3rd half-life (18 hours): 50 g / 2 = 25 g
- After 4th half-life (24 hours): 25 g / 2 = 12.5 g
3. Round to Nearest Integer:
- 12.5 g rounds to 13 g
Final Result
Therefore, the mass of the radioisotope remaining after 24 hours is approximately 13 g. This decay process illustrates the exponential nature of radioisotope decay, with the remaining mass decreasing by half with each successive half-life.
The half-life of a radioisotope is the time required for half of the isotope to decay. In this case, the half-life is 6 hours.
Calculation of Remaining Mass
To find the remaining mass after 24 hours, follow these steps:
1. Determine the Number of Half-Lives:
- Total time = 24 hours
- Half-life = 6 hours
- Number of half-lives = Total time / Half-life = 24 hours / 6 hours = 4
2. Calculate Remaining Mass:
- Initial mass = 200 g
- After each half-life, the mass is halved:
- After 1st half-life (6 hours): 200 g / 2 = 100 g
- After 2nd half-life (12 hours): 100 g / 2 = 50 g
- After 3rd half-life (18 hours): 50 g / 2 = 25 g
- After 4th half-life (24 hours): 25 g / 2 = 12.5 g
3. Round to Nearest Integer:
- 12.5 g rounds to 13 g
Final Result
Therefore, the mass of the radioisotope remaining after 24 hours is approximately 13 g. This decay process illustrates the exponential nature of radioisotope decay, with the remaining mass decreasing by half with each successive half-life.
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The half-life of a radioisotope is six hours. If the initial mass of ...
Radioactive decay follows first order kinetics.
Number of half-lives (t1/2) = 24/6 = 4
Nt = N0(1/2)4 = N0/16.
1 g of the element will reduce to 1/16g.
Therefore, mass of the radioisotope remaining 1/16 x 200 = 12.5 g = 13 g
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The half-life of a radioisotope is six hours. If the initial mass of the isotope is 200 g, then the mass (in g) remaining after 24 hours undecayed will be (Nearest integer)Correct answer is '13'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The half-life of a radioisotope is six hours. If the initial mass of the isotope is 200 g, then the mass (in g) remaining after 24 hours undecayed will be (Nearest integer)Correct answer is '13'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The half-life of a radioisotope is six hours. If the initial mass of the isotope is 200 g, then the mass (in g) remaining after 24 hours undecayed will be (Nearest integer)Correct answer is '13'. Can you explain this answer?.
The half-life of a radioisotope is six hours. If the initial mass of the isotope is 200 g, then the mass (in g) remaining after 24 hours undecayed will be (Nearest integer)Correct answer is '13'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The half-life of a radioisotope is six hours. If the initial mass of the isotope is 200 g, then the mass (in g) remaining after 24 hours undecayed will be (Nearest integer)Correct answer is '13'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The half-life of a radioisotope is six hours. If the initial mass of the isotope is 200 g, then the mass (in g) remaining after 24 hours undecayed will be (Nearest integer)Correct answer is '13'. Can you explain this answer?.
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