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The initial number of atorms of radioactive element with half 100 days, is 9.6 * 10 ^ 26 The num of atoms remaining undecayed a 500 days, will be: [1] 19.2 * 10 ^ 25 [2] 9.6 * 10 ^ 25 [3] 3.84 * 10 ^ 25 [4] 3 * 10 ^ 25?
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The initial number of atorms of radioactive element with half 100 days...
Understanding Radioactive Decay
To determine the number of remaining undecayed atoms of a radioactive element after a certain period, we can use the concept of half-life. The half-life is the time required for half of the radioactive atoms to decay.
Given Information:
- Initial number of atoms: 9.6 * 10^26
- Half-life: 100 days
- Total time: 500 days
Calculating the Number of Half-Lives:
- Total time (500 days) divided by half-life (100 days) gives us the number of half-lives:
500 days / 100 days = 5 half-lives
Calculating Remaining Atoms:
- After each half-life, the amount of radioactive material is halved. Therefore, after 5 half-lives, the remaining number of atoms can be calculated as follows:
Remaining atoms = Initial atoms * (1/2)^(number of half-lives)
Remaining atoms = 9.6 * 10^26 * (1/2)^5
Calculation Steps:
- First, calculate (1/2)^5:
(1/2)^5 = 1/32
- Next, multiply the initial number of atoms by this fraction:
Remaining atoms = 9.6 * 10^26 * (1/32)
- 9.6 / 32 = 0.3
- Therefore, Remaining atoms = 0.3 * 10^26 = 3.0 * 10^25
Conclusion:
- The number of undecayed atoms remaining after 500 days is 3 * 10^25.
Final Answer:
- The correct choice is [4] 3 * 10^25.
To determine the number of remaining undecayed atoms of a radioactive element after a certain period, we can use the concept of half-life. The half-life is the time required for half of the radioactive atoms to decay.
Given Information:
- Initial number of atoms: 9.6 * 10^26
- Half-life: 100 days
- Total time: 500 days
Calculating the Number of Half-Lives:
- Total time (500 days) divided by half-life (100 days) gives us the number of half-lives:
500 days / 100 days = 5 half-lives
Calculating Remaining Atoms:
- After each half-life, the amount of radioactive material is halved. Therefore, after 5 half-lives, the remaining number of atoms can be calculated as follows:
Remaining atoms = Initial atoms * (1/2)^(number of half-lives)
Remaining atoms = 9.6 * 10^26 * (1/2)^5
Calculation Steps:
- First, calculate (1/2)^5:
(1/2)^5 = 1/32
- Next, multiply the initial number of atoms by this fraction:
Remaining atoms = 9.6 * 10^26 * (1/32)
- 9.6 / 32 = 0.3
- Therefore, Remaining atoms = 0.3 * 10^26 = 3.0 * 10^25
Conclusion:
- The number of undecayed atoms remaining after 500 days is 3 * 10^25.
Final Answer:
- The correct choice is [4] 3 * 10^25.
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The initial number of atorms of radioactive element with half 100 days, is 9.6 * 10 ^ 26 The num of atoms remaining undecayed a 500 days, will be: [1] 19.2 * 10 ^ 25 [2] 9.6 * 10 ^ 25 [3] 3.84 * 10 ^ 25 [4] 3 * 10 ^ 25?
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The initial number of atorms of radioactive element with half 100 days, is 9.6 * 10 ^ 26 The num of atoms remaining undecayed a 500 days, will be: [1] 19.2 * 10 ^ 25 [2] 9.6 * 10 ^ 25 [3] 3.84 * 10 ^ 25 [4] 3 * 10 ^ 25? for DSSSB TGT/PGT/PRT 2025 is part of DSSSB TGT/PGT/PRT preparation. The Question and answers have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus. Information about The initial number of atorms of radioactive element with half 100 days, is 9.6 * 10 ^ 26 The num of atoms remaining undecayed a 500 days, will be: [1] 19.2 * 10 ^ 25 [2] 9.6 * 10 ^ 25 [3] 3.84 * 10 ^ 25 [4] 3 * 10 ^ 25? covers all topics & solutions for DSSSB TGT/PGT/PRT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The initial number of atorms of radioactive element with half 100 days, is 9.6 * 10 ^ 26 The num of atoms remaining undecayed a 500 days, will be: [1] 19.2 * 10 ^ 25 [2] 9.6 * 10 ^ 25 [3] 3.84 * 10 ^ 25 [4] 3 * 10 ^ 25?.
The initial number of atorms of radioactive element with half 100 days, is 9.6 * 10 ^ 26 The num of atoms remaining undecayed a 500 days, will be: [1] 19.2 * 10 ^ 25 [2] 9.6 * 10 ^ 25 [3] 3.84 * 10 ^ 25 [4] 3 * 10 ^ 25? for DSSSB TGT/PGT/PRT 2025 is part of DSSSB TGT/PGT/PRT preparation. The Question and answers have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus. Information about The initial number of atorms of radioactive element with half 100 days, is 9.6 * 10 ^ 26 The num of atoms remaining undecayed a 500 days, will be: [1] 19.2 * 10 ^ 25 [2] 9.6 * 10 ^ 25 [3] 3.84 * 10 ^ 25 [4] 3 * 10 ^ 25? covers all topics & solutions for DSSSB TGT/PGT/PRT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The initial number of atorms of radioactive element with half 100 days, is 9.6 * 10 ^ 26 The num of atoms remaining undecayed a 500 days, will be: [1] 19.2 * 10 ^ 25 [2] 9.6 * 10 ^ 25 [3] 3.84 * 10 ^ 25 [4] 3 * 10 ^ 25?.
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