A 1.00-g sample of samarium emits particles at a rate of 120 particles per second. , whose natural abundance in bulk samarium is 15.0%, is the responsible isotope. We have to calculate the half-life of this isotope.

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The molar mass of samarium, .

Therefore, the number of atoms in 1.00 g sample of samarium will be

It is given that the natural abundance of in bulk samarium is 15.0%.

Therefore, 1.00 g of natural samarium will contain nuclides. As the observed decay rate of particles in 1.00 g of samarium is 120 per second, the decay constant of will be

The half-life of particle decay of will therefore be

As, the half-life of particle decay of will be