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Question: A radioactive substance X decays into another radioactive substance Y. Initially only X was present....

A radioactive substance X decays into another radioactive substance Y. Initially only X was present. lx and ly are the disintegration constants of X and Y. Nx and Ny are the number of nuclei of X and Y at any time t. Number of nuclei Ny will be maximum when:

A

NyNx−Ny\frac{N_{y}}{N_{x} - N_{y}}=λyλx−λy\frac{\lambda_{y}}{\lambda_{x} - \lambda_{y}}

B

NxNx−Ny\frac{N_{x}}{N_{x} - N_{y}}=λxλx−λy\frac{\lambda_{x}}{\lambda_{x} - \lambda_{y}}

C

lyNy = lxNx

D

lyNx = lxNy

Answer

lyNy = lxNx

Explanation

Solution

Net rate of formation of Y at any time t is:

= lxNx – lyNy Ny is maximum when = 0

or lyNy = lxNx