The activity of a freshly prepared radioactive sample is disintegrations per second, whose mean life is . The mass of an atom of this radioisotope is . The mass (in mg) of the radioactive sample is [2011]

Question

The activity of a freshly prepared radioactive sample is $10^{10}$ disintegrations per second, whose mean life is $10^{9} s$ . The mass of an atom of this radioisotope is $10^{- 25} kg$ . The mass (in mg) of the radioactive sample is [2011]

Smart Achievers · Accepted Answer

(1)

$We know that,$ $10^{9} s$ $= λ N = \frac{1}{T_{mean}} N$ $[∵ λ = \frac{1}{T_{mean}}]$

$∴$ $10^{10} = \frac{1}{10^{9}} \times N$

$∴$ $N = 10^{19}$

$i.e.,$ $10^{19}$ $radioactive atoms are present in the freshly prepared sample.$

$∴$ $Mass of the sample = N \times mass of one atom$

$= 10^{19} \times 10^{- 25} kg = 10^{- 6} kg = 1 mg$

Solution

Q.
The activity of a freshly prepared radioactive sample is $10^{10}$ disintegrations per second, whose mean life is $10^{9} s$ . The mass of an atom of this radioisotope is $10^{- 25} kg$ . The mass (in mg) of the radioactive sample is [2011]

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Solution

Q. 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 [2011]

Ans. (1) We know that, |dNdt|=λN=1TmeanN [∵ λ=1Tmean] ∴ 1010=1109×N ∴ N=1019 i.e., 1019 radioactive atoms are present in the freshly prepared sample. ∴ Mass of the sample=N×mass of one atom =1019×10-25 kg=10-6 kg=1 mg

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Q.
The activity of a freshly prepared radioactive sample is $10^{10}$ disintegrations per second, whose mean life is $10^{9} s$ . The mass of an atom of this radioisotope is $10^{- 25} kg$ . The mass (in mg) of the radioactive sample is [2011]