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The activity of a freshly prepared radioactive sample is 1010 disintegrations per second, whose mean life is
109 s. The mass of an atom of this radioisotope is 10-25 kg. The mass (in mg) of the radioactive sample is
109 s. The mass of an atom of this radioisotope is 10-25 kg. The mass (in mg) of the radioactive sample is
Correct answer is '1'. Can you explain this answer?
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The activity of a freshly prepared radioactive sample is 1010 disinteg...
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The activity of a freshly prepared radioactive sample is 1010 disinteg...
Mass of the Radioactive Sample
Given:
Activity (A) = 10^10 disintegrations per second
Mean life (τ) = 10^9 s
Mass of an atom (m) = 10^-25 kg
We need to find the mass of the radioactive sample in milligrams (mg).
### 1. Finding the Decay Constant (λ)
The decay constant (λ) is related to the mean life (τ) by the formula:
λ = 1 / τ
Substituting the given value of τ:
λ = 1 / (10^9 s)
λ = 10^-9 s^-1
### 2. Finding the Number of Atoms (N)
The activity (A) is defined as the number of disintegrations per second. It is related to the decay constant (λ) and the number of radioactive atoms (N) by the formula:
A = λN
Rearranging the formula to solve for N:
N = A / λ
Substituting the given values of A and λ:
N = (10^10 disintegrations per second) / (10^-9 s^-1)
N = 10^19 radioactive atoms
### 3. Finding the Mass of the Sample (M)
The mass of the sample (M) is related to the number of atoms (N) and the mass of a single atom (m) by the formula:
M = N * m
Substituting the given values of N and m:
M = (10^19 radioactive atoms) * (10^-25 kg/atom)
M = 10^-6 kg = 1 mg
### Conclusion
The mass of the radioactive sample is 1 milligram (mg).
Given:
Activity (A) = 10^10 disintegrations per second
Mean life (τ) = 10^9 s
Mass of an atom (m) = 10^-25 kg
We need to find the mass of the radioactive sample in milligrams (mg).
### 1. Finding the Decay Constant (λ)
The decay constant (λ) is related to the mean life (τ) by the formula:
λ = 1 / τ
Substituting the given value of τ:
λ = 1 / (10^9 s)
λ = 10^-9 s^-1
### 2. Finding the Number of Atoms (N)
The activity (A) is defined as the number of disintegrations per second. It is related to the decay constant (λ) and the number of radioactive atoms (N) by the formula:
A = λN
Rearranging the formula to solve for N:
N = A / λ
Substituting the given values of A and λ:
N = (10^10 disintegrations per second) / (10^-9 s^-1)
N = 10^19 radioactive atoms
### 3. Finding the Mass of the Sample (M)
The mass of the sample (M) is related to the number of atoms (N) and the mass of a single atom (m) by the formula:
M = N * m
Substituting the given values of N and m:
M = (10^19 radioactive atoms) * (10^-25 kg/atom)
M = 10^-6 kg = 1 mg
### Conclusion
The mass of the radioactive sample is 1 milligram (mg).
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The activity of a freshly prepared radioactive sample is 1010 disintegrations per second, whose mean life is109 s. The mass of an atom of this radioisotope is 10-25 kg. The mass (in mg) of the radioactive sample isCorrect answer is '1'. Can you explain this answer?
Question Description
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