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

Who invented radioactivity ? 

Half life of $B{i^{210}}$ is $5$ days. If we start with $50,000$ atoms of this isotope, the number of atoms left over after $10$ days is

After five half lives what will be the fraction of initial substance

A element used for radioactive carbon dating for more than $5600$ years is

A parent nucleus $X$ is decaying into daughter nucleus $Y$ which in turn decays to $Z$. The half lives of $X$ and $Y$ are $40000 \,yr$ and $20 \,yr$, respectively. In a certain sample, it is found that the number of $Y$ nuclei hardly changes with time. If the number of $X$ nuclei in the sample is $4 \times 10^{20}$, the number of $Y$ nuclei present in it is