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Q.

The half-value period of RaB (Pb 214 82 ) is 26.8 minutes. The mass of one curie of RaB is

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a

3.71 x 1010 g

b

3.71 x 10-10 g

c

8.61 x 1010 g

d

3.064 x 10-8 g

answer is D.

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Detailed Solution

Here T = 26.8 minutes= 26.8 x 60 sec∴  Decay constant,λ=0.693T=0.69326.8 x 60 =4.32 x 104sec-1Now 1 curie is equal to 3.71 x 1010 disintegrations per second.∴λ=3.71 x 1010If N be the number of atoms in one curie, then -dNdt=λNor 3.71 x 1010=4.31 x 10-4 N∴N=3.71 x 10104.31 x 10-4=8.607 x 1013Further, atomic weight of RaB = 214 and Avogadro's number = 6.025 x 1023Mass of one atom =2146.025 x 1023Mass of N atoms =2146.025 x 1023 x 8.607 x 1013 =3.064 x 10-8g
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The half-value period of RaB (Pb 214 82 ) is 26.8 minutes. The mass of one curie of RaB is