If the atomic number (Z) and mass number (A) of an element X are related by the equation A+Z= 46 and the total number of neutrons in one atom of X is 16, then the total number of protons and electrons in one atom of element X='a'. Find value of 'a'

Answer

To solve the problem, we will break it down step by step.

### Step 1: Understand the relationship between mass number (A), atomic number (Z), and neutrons.
The mass number (A) is the total number of protons and neutrons in an atom. The atomic number (Z) is the number of protons in the atom. The number of neutrons (N) can be calculated using the formula:
\[ N = A - Z \]

### Step 2: Use the given equation.
We are given the equation:
\[ A + Z = 46 \]
We can rearrange this equation to express A in terms of Z:
\[ A = 46 - Z \]

### Step 3: Use the information about neutrons.
We know that the total number of neutrons in one atom of X is 16. Therefore, we can substitute N = 16 into the earlier formula:
\[ N = A - Z \]
This gives us:
\[ 16 = A - Z \]

### Step 4: Set up a system of equations.
Now we have two equations:
1. \( A + Z = 46 \) (Equation 1)
2. \( A - Z = 16 \) (Equation 2)

### Step 5: Solve the system of equations.
We can add Equation 1 and Equation 2:
\[ (A + Z) + (A - Z) = 46 + 16 \]
This simplifies to:
\[ 2A = 62 \]
Now, divide both sides by 2:
\[ A = 31 \]

### Step 6: Find Z using A.
Now we can substitute A back into Equation 1 to find Z:
\[ 31 + Z = 46 \]
Subtract 31 from both sides:
\[ Z = 15 \]

### Step 7: Find the total number of protons and electrons.
In a neutral atom, the number of protons is equal to the number of electrons. Therefore, the total number of protons and electrons is:
\[ \text{Total} = Z + Z = 2Z = 2 \times 15 = 30 \]

### Final Answer:
The total number of protons and electrons in one atom of element X is \( a = 30 \).

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