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Question: When secular radioactive equilibrium is reached between Radium and Uranium then which of the followi...

When secular radioactive equilibrium is reached between Radium and Uranium then which of the following relation hold true. Given : lR® decay constant of radium NR® No. of nuclei of RadiumlU® decay constant of Uranium NU® No. of nuclei of Uranium

A

lR/lU = NU/NR

B

lR/lU = NR/NU

C

λRλU\frac{\lambda_{R}}{\lambda_{U}}= NR/NU\sqrt{N_{R}/N_{U}}

D

lR/lU = NU/NR\sqrt{N_{U}/N_{R}}

Answer

lR/lU = NU/NR

Explanation

Solution

Successive disintegration

dNBdt\frac { \mathrm { dN } _ { \mathrm { B } } } { \mathrm { dt } } = lANA – lBNB in equilibrium dNBdt\frac { \mathrm { dN } _ { \mathrm { B } } } { \mathrm { dt } } = 0 i.e. rate of production of B equals the rate of disintegration of B