A radio isotope ‘$X$’ with a half life $1.4\times {10}^9$ years decays to ‘$Y$’ which is stable. A sample of the rock from a cave was found to contain ‘$X$’ and ‘$Y$’ in the ratio $1:7$. The age of the rock is

A nuclear reaction is given below.
${}_1\mathrm{H}^1+{}_1\mathrm{H}^1+{}_1\mathrm{H}^2\to X+{}_1{}^{}\mathrm{e}^0+\mathrm{energy}$ 
The emitted particle $X$ is

Originally the radioactive beta decay was thought as a decay of a nucleus with the emission of electrons only (case $\mathrm{I}$). However, in addition to electron, another (nearly) massless and electrically neutral particle is also emitted (case $\mathrm{II}$). Based on the figure below, which of the following is correct.