It is known that atom contain protons. Neutrons and electrons. If the mass of neutron is assumed to half of its orginal value where as that of proton is assumed to be twice of its original value then the atomic mass of `._(6)^(14)C` will be :-

Options

A. same
B. `25%` more
C. `14.28%` more
D. `28.5%` more

Answer

To solve the problem, we need to calculate the new atomic mass of carbon-14 (represented as \( _{6}^{14}C \)) after adjusting the masses of protons and neutrons as specified in the question.

### Step-by-Step Solution:

1. **Identify the number of protons and neutrons in carbon-14**:
- Carbon has an atomic number of 6, which means it has 6 protons.
- The mass number of carbon-14 is 14, which means it has \( 14 - 6 = 8 \) neutrons.

2. **Original masses of protons and neutrons**:
- The mass of a proton (original) is approximately 1 amu.
- The mass of a neutron (original) is also approximately 1 amu.

3. **Adjust the masses according to the problem**:
- The mass of a neutron is assumed to be half of its original value:
\[ \text{New mass of neutron} = \frac{1}{2} \text{ amu} = 0.5 \text{ amu} \]
- The mass of a proton is assumed to be twice its original value:
\[ \text{New mass of proton} = 2 \times 1 \text{ amu} = 2 \text{ amu} \]

4. **Calculate the new total mass of carbon-14**:
- Total mass contributed by protons:
\[ \text{Total mass from protons} = \text{Number of protons} \times \text{New mass of proton} = 6 \times 2 \text{ amu} = 12 \text{ amu} \]
- Total mass contributed by neutrons:
\[ \text{Total mass from neutrons} = \text{Number of neutrons} \times \text{New mass of neutron} = 8 \times 0.5 \text{ amu} = 4 \text{ amu} \]
- Therefore, the new atomic mass of carbon-14 is:
\[ \text{New atomic mass} = \text{Total mass from protons} + \text{Total mass from neutrons} = 12 \text{ amu} + 4 \text{ amu} = 16 \text{ amu} \]

5. **Calculate the percentage increase in atomic mass**:
- The original atomic mass of carbon-14 is 14 amu.
- The new atomic mass is 16 amu.
- The increase in mass is:
\[ \text{Increase} = \text{New atomic mass} - \text{Original atomic mass} = 16 \text{ amu} - 14 \text{ amu} = 2 \text{ amu} \]
- The percentage increase is calculated as:
\[ \text{Percentage increase} = \left( \frac{\text{Increase}}{\text{Original atomic mass}} \right) \times 100 = \left( \frac{2}{14} \right) \times 100 \approx 14.29\% \]

### Final Answer:
The atomic mass of \( _{6}^{14}C \) after the adjustments will be approximately **16 amu**, and the percentage increase in atomic mass is approximately **14.29%**.