Periodic Table Group of Element Produced in Nuclear Reaction

To find the group number of element $\text{X}$ in the periodic table, we start by determining its atomic number ($Z$) and mass number ($A$) using the principles of conservation of mass number and atomic number in nuclear reactions.

The given nuclear reaction is: $^{63}_{29}\text{Cu} + \,^{1}_{1}\text{H} \rightarrow 6\,^{1}_{0}\text{n} + \,^{4}_{2}\text{He} + 2\,^{1}_{1}\text{H} + \,^{A}_{Z}\text{X}$

Step 1: Conservation of Mass Number ($A$)

Sum of mass numbers on the reactant side = Sum of mass numbers on the product side

$63 + 1 = 6(1) + 4 + 2(1) + A$ $64 = 6 + 4 + 2 + A$ $64 = 12 + A$ $A = 52$

Step 2: Conservation of Atomic Number ($Z$)

Sum of atomic numbers on the reactant side = Sum of atomic numbers on the product side

$29 + 1 = 6(0) + 2 + 2(1) + Z$ $30 = 0 + 2 + 2 + Z$ $30 = 4 + Z$ $Z = 26$

Step 3: Identification of Element $\text{X}$ and its Group Number

An atomic number of $Z = 26$ corresponds to Iron ($\text{Fe}$).

The electronic configuration of Iron ($\text{Fe}$, $Z = 26$) is: $[\text{Ar}]\,3d^6\,4s^2$

For $d$-block elements, the group number in the modern periodic table is calculated as: $\text{Group number} = \text{number of } (n-1)d \text{ electrons} + \text{number of } ns \text{ electrons}$ $\text{Group number} = 6 + 2 = 8$

Thus, element $\text{X}$ belongs to group 8.