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The activity of a freshly prepared radioactive sample is 1010 disintegrations per second, whose mean life is 109s. The mass of an atom of this radioisotope is 10–25 kg. The mass (in mg) of the radioactive sample is
- a)1
- b)3
- c)5
- d)6
Correct answer is option 'A'. Can you explain this answer?
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The activity of a freshly prepared radioactive sample is 1010 disinte...
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i.e. 1019 radioactive atoms are present in the freshly prepared sample.
The mass of the sample
= 1019 × 10–25 kg = 10–6kg = 1 mg
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The activity of a freshly prepared radioactive sample is 1010 disinte...
Given:
Activity of the radioactive sample = 10^10 disintegrations/s
Mean life of the radioactive sample = 10^9 s
Mass of one atom of the radioisotope = 10^-25 kg
We know that activity (A) = λN
where λ is the decay constant and N is the number of radioactive nuclei.
Also, mean life (τ) = 1/λ
From the given data, we can calculate the decay constant as:
λ = 1/τ = 1/(10^9 s) = 10^-9 s^-1
We can also calculate the number of radioactive nuclei (N) using the activity:
A = λN
N = A/λ = (10^10 disintegrations/s)/(10^-9 s^-1) = 10^19 nuclei
Now, we can calculate the mass of the radioactive sample as:
Mass = N x mass of one atom
Mass = (10^19 nuclei) x (10^-25 kg/nucleus) = 10^-6 kg = 1 mg
Therefore, the mass of the radioactive sample is 1 mg, which is option (A).
Activity of the radioactive sample = 10^10 disintegrations/s
Mean life of the radioactive sample = 10^9 s
Mass of one atom of the radioisotope = 10^-25 kg
We know that activity (A) = λN
where λ is the decay constant and N is the number of radioactive nuclei.
Also, mean life (τ) = 1/λ
From the given data, we can calculate the decay constant as:
λ = 1/τ = 1/(10^9 s) = 10^-9 s^-1
We can also calculate the number of radioactive nuclei (N) using the activity:
A = λN
N = A/λ = (10^10 disintegrations/s)/(10^-9 s^-1) = 10^19 nuclei
Now, we can calculate the mass of the radioactive sample as:
Mass = N x mass of one atom
Mass = (10^19 nuclei) x (10^-25 kg/nucleus) = 10^-6 kg = 1 mg
Therefore, the mass of the radioactive sample is 1 mg, which is option (A).
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The activity of a freshly prepared radioactive sample is 1010 disintegrations per second, whose mean life is 109s. The mass of an atom of this radioisotope is 10–25 kg. The mass (in mg) of the radioactive sample isa)1b)3c)5d)6Correct answer is option 'A'. Can you explain this answer?
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