Total number of protons, neutrons and electrons present in 14 mg of `._(6)C^(14)` is :
(Take `N_(A) = 6 xx 10^(23))`

Options

A. `1.2 xx 10^(22)`
B. `1.2 xx 10^(25)`
C. `7.2 xx 10^(21)`
D. `1.08 xx 10^(22)`

Answer

To find the total number of protons, neutrons, and electrons present in 14 mg of \( _{6}^{14}C \) (Carbon-14), we can follow these steps:

### Step 1: Determine the number of moles of Carbon-14 in 14 mg
First, we need to convert the mass of Carbon-14 from milligrams to grams:
\[ 14 \text{ mg} = 0.014 \text{ g} \]

Next, we calculate the molar mass of Carbon-14. The molar mass of Carbon-14 is approximately 14 g/mol.

Now, we can calculate the number of moles of Carbon-14:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} = \frac{0.014 \text{ g}}{14 \text{ g/mol}} = 0.001 \text{ moles} \]

### Step 2: Calculate the total number of atoms in 0.001 moles of Carbon-14
Using Avogadro's number (\( N_A = 6.022 \times 10^{23} \) atoms/mol), we can find the total number of atoms:
\[ \text{Total number of atoms} = \text{Number of moles} \times N_A = 0.001 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} = 6.022 \times 10^{20} \text{ atoms} \]

### Step 3: Determine the number of protons, neutrons, and electrons in Carbon-14
For Carbon-14:
- The atomic number (number of protons) is 6.
- The number of neutrons can be calculated as:
\[ \text{Number of neutrons} = \text{Mass number} - \text{Number of protons} = 14 - 6 = 8 \]
- The number of electrons in a neutral atom is equal to the number of protons, which is also 6.

### Step 4: Calculate the total number of protons, neutrons, and electrons
Now we can calculate the total number of protons, neutrons, and electrons in 14 mg of Carbon-14:
- Total protons = Number of atoms × Number of protons per atom
\[ \text{Total protons} = 6.022 \times 10^{20} \text{ atoms} \times 6 = 3.6132 \times 10^{21} \text{ protons} \]

- Total neutrons = Number of atoms × Number of neutrons per atom
\[ \text{Total neutrons} = 6.022 \times 10^{20} \text{ atoms} \times 8 = 4.8176 \times 10^{21} \text{ neutrons} \]

- Total electrons = Number of atoms × Number of electrons per atom
\[ \text{Total electrons} = 6.022 \times 10^{20} \text{ atoms} \times 6 = 3.6132 \times 10^{21} \text{ electrons} \]

### Final Answer
- Total Protons: \( 3.6132 \times 10^{21} \)
- Total Neutrons: \( 4.8176 \times 10^{21} \)
- Total Electrons: \( 3.6132 \times 10^{21} \)