What is the half-life period of a radioactive material if its activity drops to $$1 / 16^{\text {th }}$$ of its initial value in 30 years?

A nucleus of mass $$M$$ at rest splits into two parts having masses $$\frac{M^{\prime}}{3}$$ and $${{2M'} \over 3}(M' < M)$$. The ratio of de Broglie wavelength of two parts will be :

Mass numbers of two nuclei are in the ratio of $$4: 3$$. Their nuclear densities will be in the ratio of

The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 disintegrations per minute. The approximate decay constant is :

$$\left(\right.$$Take $$\left.\log _{10} 1.88=0.274\right)$$