Question

If ${}_Z^{}X_{}^M + {}_2^{}H{e^4} \to {}_{15}^{}P_{}^{30} + {}_0^{}n_{}^1$, then:
A. Z=12, M=27
B. Z=13, M=27
C. Z=12, M=17
D. Z=13, M=28

Answer 1

We have a reaction where X and He react together to form P and a neutron. So the sum of atomic numbers of the reactants must be equal to the sum of atomic numbers of the products and the same with their atomic weights. Atomic number is mentioned below the symbol of the atom and atomic weight is mentioned above the symbol of the atom.

Complete step by step answer:
We are given a reaction ${}_Z^{}X_{}^M + {}_2^{}H{e^4} \to {}_{15}^{}P_{}^{30} + {}_0^{}n_{}^1$
In the above reaction, X reacts with Helium (He) to form Phosphorus (P) and a neutron (n).
The atomic number and atomic weight of Helium are 2 and 4 respectively; the atomic number and atomic weight of Phosphorus are 15 and 30 respectively; the atomic number and atomic weight of a neutron are 0 and 1 respectively. We need to find the atomic number Z and atomic weight M of the element X.
The sum of atomic numbers of the reactants is $Z + 2$ and the sum of atomic numbers of the products is $15 + 0 = 15$. As matter is neither created nor destroyed in reaction, these both sums must be equal.
This means $Z + 2 = 15$
$\therefore Z = 15 - 2 = 13$
In the same way, the sum of atomic weights of the reactants is $M + 4$ and the sum of atomic weights of the products is $30 + 1 = 31$
These two sums must be equal.
$\to M + 4 = 31$
$\therefore M = 31 - 4 = 27$
Therefore, the value of Z is 13, and the value of M is 27, this means X is Aluminum as its atomic number is 13.
Hence, the correct option is Option B.

Note: For atoms, the weight is atomic weight whereas for molecules and compounds the weight is molecular weight. The mass of a neutron is 1, same as a proton whereas an electron has no mass. The charge of a neutron is 0, whereas a proton has a positive charge and an electron has a negative charge.