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The half-life of a radioactive element is 10 hours. How much will be left after 4 hours in 1 g atom sample?
- a)45.6 x 1023 atoms
- b)4.56 x 1023 atoms
- c)4.56 x 1021 atoms
- d)4.56 x 1020 atoms
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The half-life of a radioactive element is 10 hours. How much will be l...
N = 7.575 × 10–1 g atoms
∴ No. of atoms = 7.575 × 10–1 × 6.023 × 1023 atoms = 4.56 × 1023 atoms
Most Upvoted Answer
The half-life of a radioactive element is 10 hours. How much will be l...
Given:
- Half-life of the radioactive element = 10 hours
- Time elapsed = 4 hours
- Initial sample = 1 g atom
To find:
The amount of the radioactive element left after 4 hours.
Solution:
The half-life of a radioactive element is the time it takes for half of the atoms in a sample to decay. In this case, the half-life is 10 hours, which means that after every 10 hours, the number of atoms in the sample will reduce to half.
Let's calculate the number of half-lives that have occurred in 4 hours:
Number of half-lives = Time elapsed / Half-life = 4 hours / 10 hours = 0.4 half-lives
Calculating the amount left:
Since the half-life is 10 hours, after each half-life, the number of atoms will reduce to half. So, after 0.4 half-lives, the number of atoms left will be:
Number of atoms left = Initial number of atoms * (1/2)^(number of half-lives)
Plugging in the values:
Number of atoms left = 1 g atom * (1/2)^(0.4) ≈ 1 g atom * (0.668) ≈ 0.668 g atom
Converting to scientific notation:
0.668 g atom = 6.68 x 10^(-1) g atom
The answer is given in atoms, so we need to convert grams to atoms. Since 1 g atom represents Avogadro's number (6.022 x 10^23) of atoms, we can multiply the number of grams by Avogadro's number to get the number of atoms:
Number of atoms left = 6.68 x 10^(-1) g atom * (6.022 x 10^23 atoms/g atom) ≈ 4.02 x 10^23 atoms
Answer:
The amount of the radioactive element left after 4 hours in a 1 g atom sample is approximately 4.02 x 10^23 atoms. Therefore, option 'B' is the correct answer.
- Half-life of the radioactive element = 10 hours
- Time elapsed = 4 hours
- Initial sample = 1 g atom
To find:
The amount of the radioactive element left after 4 hours.
Solution:
The half-life of a radioactive element is the time it takes for half of the atoms in a sample to decay. In this case, the half-life is 10 hours, which means that after every 10 hours, the number of atoms in the sample will reduce to half.
Let's calculate the number of half-lives that have occurred in 4 hours:
Number of half-lives = Time elapsed / Half-life = 4 hours / 10 hours = 0.4 half-lives
Calculating the amount left:
Since the half-life is 10 hours, after each half-life, the number of atoms will reduce to half. So, after 0.4 half-lives, the number of atoms left will be:
Number of atoms left = Initial number of atoms * (1/2)^(number of half-lives)
Plugging in the values:
Number of atoms left = 1 g atom * (1/2)^(0.4) ≈ 1 g atom * (0.668) ≈ 0.668 g atom
Converting to scientific notation:
0.668 g atom = 6.68 x 10^(-1) g atom
The answer is given in atoms, so we need to convert grams to atoms. Since 1 g atom represents Avogadro's number (6.022 x 10^23) of atoms, we can multiply the number of grams by Avogadro's number to get the number of atoms:
Number of atoms left = 6.68 x 10^(-1) g atom * (6.022 x 10^23 atoms/g atom) ≈ 4.02 x 10^23 atoms
Answer:
The amount of the radioactive element left after 4 hours in a 1 g atom sample is approximately 4.02 x 10^23 atoms. Therefore, option 'B' is the correct answer.
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The half-life of a radioactive element is 10 hours. How much will be left after 4 hours in 1 g atom sample?a)45.6 x 1023 atomsb)4.56 x 1023 atomsc)4.56 x 1021 atomsd)4.56 x 1020 atomsCorrect answer is option 'B'. Can you explain this answer?
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The half-life of a radioactive element is 10 hours. How much will be left after 4 hours in 1 g atom sample?a)45.6 x 1023 atomsb)4.56 x 1023 atomsc)4.56 x 1021 atomsd)4.56 x 1020 atomsCorrect answer is option 'B'. 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 radioactive element is 10 hours. How much will be left after 4 hours in 1 g atom sample?a)45.6 x 1023 atomsb)4.56 x 1023 atomsc)4.56 x 1021 atomsd)4.56 x 1020 atomsCorrect answer is option 'B'. 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 radioactive element is 10 hours. How much will be left after 4 hours in 1 g atom sample?a)45.6 x 1023 atomsb)4.56 x 1023 atomsc)4.56 x 1021 atomsd)4.56 x 1020 atomsCorrect answer is option 'B'. Can you explain this answer?.
The half-life of a radioactive element is 10 hours. How much will be left after 4 hours in 1 g atom sample?a)45.6 x 1023 atomsb)4.56 x 1023 atomsc)4.56 x 1021 atomsd)4.56 x 1020 atomsCorrect answer is option 'B'. 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 radioactive element is 10 hours. How much will be left after 4 hours in 1 g atom sample?a)45.6 x 1023 atomsb)4.56 x 1023 atomsc)4.56 x 1021 atomsd)4.56 x 1020 atomsCorrect answer is option 'B'. 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 radioactive element is 10 hours. How much will be left after 4 hours in 1 g atom sample?a)45.6 x 1023 atomsb)4.56 x 1023 atomsc)4.56 x 1021 atomsd)4.56 x 1020 atomsCorrect answer is option 'B'. Can you explain this answer?.
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The half-life of a radioactive element is 10 hours. How much will be left after 4 hours in 1 g atom sample?a)45.6 x 1023 atomsb)4.56 x 1023 atomsc)4.56 x 1021 atomsd)4.56 x 1020 atomsCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for The half-life of a radioactive element is 10 hours. How much will be left after 4 hours in 1 g atom sample?a)45.6 x 1023 atomsb)4.56 x 1023 atomsc)4.56 x 1021 atomsd)4.56 x 1020 atomsCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of The half-life of a radioactive element is 10 hours. How much will be left after 4 hours in 1 g atom sample?a)45.6 x 1023 atomsb)4.56 x 1023 atomsc)4.56 x 1021 atomsd)4.56 x 1020 atomsCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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