In 14g of `^14 C_6` isotope of carbon, the number of protons, neutrons and electrons are

Options

A. `48xx10^(23), 48xx10^(23),36xx10^(21)`
B. `36xx10^(23), 36xx10^(23),36xx10^(21)`
C. `36xx10^(23), 48xx10^(23),36xx10^(23)`
D. `48xx10^(23), 48xx10^(23),48xx10^(23)`

Answer

To solve the problem of finding the number of protons, neutrons, and electrons in 14 grams of the isotope \(^{14}C_6\), we can follow these steps:

### Step 1: Identify the number of protons
The notation \(^{14}C_6\) indicates that this is the carbon isotope with a mass number of 14. The subscript 6 represents the atomic number, which is the number of protons in the nucleus of the atom.

**Calculation:**
- Number of protons = 6 (from the atomic number)

### Step 2: Calculate the number of neutrons
The number of neutrons can be calculated using the formula:
\[ \text{Number of neutrons} = \text{Mass number} - \text{Number of protons} \]

**Calculation:**
- Mass number = 14
- Number of protons = 6
- Number of neutrons = 14 - 6 = 8

### Step 3: Determine the number of electrons
In a neutral atom, the number of electrons is equal to the number of protons.

**Calculation:**
- Number of electrons = Number of protons = 6

### Step 4: Calculate the total number of atoms in 14 grams
The atomic mass of \(^{14}C\) is 14 g/mol. Therefore, 14 grams of \(^{14}C\) corresponds to 1 mole of carbon atoms.

**Calculation:**
- Number of atoms in 14 grams = 1 mole = \(6.022 \times 10^{23}\) atoms (Avogadro's number)

### Step 5: Calculate the total number of protons, neutrons, and electrons in 14 grams
Now, we can calculate the total number of protons, neutrons, and electrons in 14 grams of \(^{14}C\).

**Total Protons:**
\[ \text{Total protons} = \text{Number of protons in one atom} \times \text{Total number of atoms} \]
\[ = 6 \times 6.022 \times 10^{23} = 36.132 \times 10^{23} \approx 3.6132 \times 10^{24} \]

**Total Neutrons:**
\[ \text{Total neutrons} = \text{Number of neutrons in one atom} \times \text{Total number of atoms} \]
\[ = 8 \times 6.022 \times 10^{23} = 48.176 \times 10^{23} \approx 4.8176 \times 10^{24} \]

**Total Electrons:**
\[ \text{Total electrons} = \text{Number of electrons in one atom} \times \text{Total number of atoms} \]
\[ = 6 \times 6.022 \times 10^{23} = 36.132 \times 10^{23} \approx 3.6132 \times 10^{24} \]

### Summary of Results
- Total Protons = \(3.6132 \times 10^{24}\)
- Total Neutrons = \(4.8176 \times 10^{24}\)
- Total Electrons = \(3.6132 \times 10^{24}\)