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. `14.28% "less"`
C. `14.28% "more"`
D. `28.56% "less"`

Answer

To solve the problem, we need to determine the new atomic mass of the isotope of carbon, \( _{6}^{14}C \), given the changes in the masses of protons and neutrons. Here’s a step-by-step solution:

### Step 1: Identify the number of protons and neutrons
- The atomic number (Z) of carbon is 6, which means it has 6 protons.
- The mass number (A) of carbon is 14. The number of neutrons can be calculated using the formula:
\[ \text{Number of neutrons} = A - Z = 14 - 6 = 8 \]

### Step 2: Determine the modified masses of protons and neutrons
- The original mass of a proton is assumed to be 1 unit. Since the mass of the proton is doubled, the new mass of a proton will be:
\[ \text{New mass of proton} = 2 \times 1 = 2 \text{ units} \]
- The original mass of a neutron is also assumed to be 1 unit. Since the mass of the neutron is halved, the new mass of a neutron will be:
\[ \text{New mass of neutron} = \frac{1}{2} \times 1 = 0.5 \text{ units} \]

### Step 3: Calculate the new atomic mass
- The new atomic mass is calculated by adding the total mass contributed by protons and neutrons:
\[ \text{New atomic mass} = (\text{Number of protons} \times \text{New mass of proton}) + (\text{Number of neutrons} \times \text{New mass of neutron}) \]
\[ = (6 \times 2) + (8 \times 0.5) = 12 + 4 = 16 \text{ units} \]

### Step 4: Calculate the percentage increase in mass
- The original atomic mass of carbon was 14 units. The percentage increase in mass can be calculated using the formula:
\[ \text{Percentage increase} = \left( \frac{\text{New mass} - \text{Original mass}}{\text{Original mass}} \right) \times 100 \]
\[ = \left( \frac{16 - 14}{14} \right) \times 100 = \left( \frac{2}{14} \right) \times 100 \approx 14.29\% \]

### Final Answer
The new atomic mass of \( _{6}^{14}C \) is 16 units, and the percentage increase in mass is approximately 14.29%.

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