The activity of a radioactive sample is $1.6\, curie$ and its half-life is $2.5 \,days$. Its activity after $10\, days$ will be ………. $curie$

After absorbing a slowly moving neutron of mass $m_N$  $(momentum $~ $0)$ a nucleus of mass $M$ breaks into two nuclei of masses $m_1$ and $3m_1$ $(4m_1 = M + m_N)$, respectively. If the de Broglie wavelength of the nucleus with mass $m_1$ is $\lambda$, then de Broglie wavelength of the other nucleus will be

The half life of $^{131}I$ is $8\, days$. Given a sample of $^{131}I$ at time $t = 0,$ we can assert that

Two radioactive materials $X_1$ and $X_2$ contain same number of nuclei. If $6\,\lambda {s^{ – 1}}$ and $4\,\lambda {s^{ – 1}}$ are the decay constants of $X_1$ and $X_2$ respectively the ratio of number of nuclei, undecayed of $X_1$ to that of $X_2$ will be $\left( {\frac{1}{e}} \right)$ after a time 

$37$ Rutherford equals