In which of the following nuclear reactions is the product incorrectly matched?

$A$ radioactive nucleus of mass $M$ emits a photon of frequency $f$ and the nucleus recoils. The recoil energy will be

In the equation ${ }_{13}^{27} Al + { }_2^4 He \longrightarrow { }_{15}^{30} P + X$,the correct symbol for $X$ is:

$A$ particle having almost zero mass and exactly zero charge is

The radius $R$ of a nucleus of mass number $A$ can be estimated by the formula $R = (1.3 \times 10^{-15}) A^{1/3} \; m$. It follows that the mass density of a nucleus is of the order of $(M_{\text{prot}} \cong M_{\text{neut}} = 1.67 \times 10^{-27} \; kg)$.

In a periodic table,the average atomic mass of magnesium is given as $24.312 \; u$. This average value is based on their relative natural abundance on Earth. The three isotopes and their masses are $_{12}^{24} Mg \; (23.98504 \; u)$,$_{12}^{25} Mg \; (24.98584 \; u)$,and $_{12}^{26} Mg \; (25.98259 \; u)$. The natural abundance of $_{12}^{24} Mg$ is $78.99 \%$. Calculate the abundances of the other two isotopes.