The periodic table consists of 18 groups. An isotope of copper, on bombardment with protons, undergoes a nuclear reaction yielding element `X` as shown below. To which group, element `X` belongs in the periodic table ?
`._(29)Cu^(63)+._(1)H^(1)rarr6._(0)n^(1)+._(2)He^(4)(alpha)+2._(1)H^(1)+._(Z)X^(A)`

Explanation

To solve the problem, we need to analyze the nuclear reaction provided and determine the properties of the resulting element \(X\). The reaction is as follows:

\[ _{29}^{63}\text{Cu} + _{1}^{1}\text{H} \rightarrow 6 \, _{0}^{1}\text{n} + _{2}^{4}\text{He} + 2 \, _{1}^{1}\text{H} + _{Z}^{A}X \]

### Step 1: Determine the Mass Number of Element \(X\)

1. **Calculate the total mass number on the reactant side:**
- Mass number of Copper (Cu) = 63
- Mass number of Hydrogen (H) = 1
- Total mass number = \(63 + 1 = 64\)

2. **Calculate the total mass number on the product side:**
- Mass number of neutrons (n) = \(6 \times 1 = 6\)
- Mass number of alpha particle (He) = 4
- Mass number of protons (H) = \(2 \times 1 = 2\)
- Let the mass number of element \(X\) be \(A\).

Therefore, the equation for mass number conservation is:
\[ 64 = 6 + 4 + 2 + A \]
Simplifying gives:
\[ 64 = 12 + A \implies A = 64 - 12 = 52 \]

### Step 2: Determine the Atomic Number of Element \(X\)

1. **Calculate the total atomic number on the reactant side:**
- Atomic number of Copper (Cu) = 29
- Atomic number of Hydrogen (H) = 1
- Total atomic number = \(29 + 1 = 30\)

2. **Calculate the total atomic number on the product side:**
- Atomic number of neutrons = 0 (neutrons have no charge)
- Atomic number of alpha particle (He) = 2
- Atomic number of protons (H) = \(2 \times 1 = 2\)
- Let the atomic number of element \(X\) be \(Z\).

Therefore, the equation for atomic number conservation is:
\[ 30 = 0 + 2 + 2 + Z \]
Simplifying gives:
\[ 30 = 4 + Z \implies Z = 30 - 4 = 26 \]

### Step 3: Identify Element \(X\)

From the calculations, we have determined:
- Mass number \(A = 52\)
- Atomic number \(Z = 26\)

The element with atomic number 26 is Iron (Fe).

### Step 4: Determine the Group of Element \(X\)

Iron (Fe) is located in the periodic table:
- It is a transition metal and belongs to the d-block.
- The group number for Iron is 8.

### Conclusion

Element \(X\) is Iron (Fe), and it belongs to group 8 in the periodic table.

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