An ion having a 4+ charge and a mass of 51.99 amu has two electrons with n=1,eight electrons with n=2,and ten electrons with n=3.Give the total number of protons present in the nucleus of the atom of metal.

Explanation

To solve the problem, we need to determine the total number of protons present in the nucleus of the metal ion described. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Given Information
We have an ion with a +4 charge, a mass of 51.99 amu, and the following electron distribution:
- 2 electrons in n=1
- 8 electrons in n=2
- 10 electrons in n=3

### Step 2: Calculate the Total Number of Electrons in the Ion
The total number of electrons in the ion (X⁴⁺) is given by the sum of the electrons in each shell:
- Electrons in n=1: 2
- Electrons in n=2: 8
- Electrons in n=3: 10

Total electrons in X⁴⁺ = 2 + 8 + 10 = 20 electrons.

### Step 3: Determine the Number of Electrons in the Neutral Atom
Since the ion has a +4 charge, it means that 4 electrons have been removed from the neutral atom (X). Therefore, to find the number of electrons in the neutral atom:
- Electrons in neutral atom (X) = Electrons in ion (X⁴⁺) + 4
- Electrons in neutral atom (X) = 20 + 4 = 24 electrons.

### Step 4: Relate Electrons to Protons
In a neutral atom, the number of protons is equal to the number of electrons. Thus, the number of protons in the neutral atom (X) is also 24.

### Step 5: Conclusion
The total number of protons present in the nucleus of the atom of the metal is 24.

### Final Answer
**Total number of protons = 24**

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