Let the mass of electron is two times, mass of proton is 1/4 and mass of neutron is 3/2 of original mass. Then, the atomic weight of `C_6^12` atom

Options

A. Increases by 37.5%
B. Decreases by 87.5%
C. Decreases by 12.5%
D. Remains same

Answer

To solve the problem, we need to calculate the atomic weight of the carbon atom \(C_6^{12}\) based on the modified masses of its constituent particles as per the question.

### Step-by-Step Solution:

1. **Identify the Original Masses:**
- The original atomic weight of carbon \(C_6^{12}\) is 12 amu.
- Carbon has 6 protons, 6 neutrons, and 6 electrons.

2. **Modified Mass of Electrons:**
- According to the problem, the mass of the electron is 2 times the original mass. However, since the mass of an electron is negligible compared to protons and neutrons, we will not consider this change in our calculations.

3. **Modified Mass of Protons:**
- The mass of the proton is given as \( \frac{1}{4} \) of the original mass.
- The original mass of a proton is approximately 1 amu.
- Therefore, the new mass of each proton is:
\[ \text{New mass of proton} = \frac{1}{4} \times 1 \text{ amu} = 0.25 \text{ amu} \]
- For 6 protons, the total mass contributed by protons is:
\[ \text{Total mass from protons} = 6 \times 0.25 \text{ amu} = 1.5 \text{ amu} \]

4. **Modified Mass of Neutrons:**
- The mass of the neutron is given as \( \frac{3}{2} \) of the original mass.
- The original mass of a neutron is approximately 1 amu.
- Therefore, the new mass of each neutron is:
\[ \text{New mass of neutron} = \frac{3}{2} \times 1 \text{ amu} = 1.5 \text{ amu} \]
- For 6 neutrons, the total mass contributed by neutrons is:
\[ \text{Total mass from neutrons} = 6 \times 1.5 \text{ amu} = 9 \text{ amu} \]

5. **Calculate Total Mass of the Carbon Atom:**
- Now, we can calculate the total mass of the carbon atom:
\[ \text{Total mass} = \text{Total mass from protons} + \text{Total mass from neutrons} + \text{Total mass from electrons} \]
- Since the mass of electrons is negligible, we can ignore it:
\[ \text{Total mass} = 1.5 \text{ amu} + 9 \text{ amu} = 10.5 \text{ amu} \]

6. **Calculate the Decrease in Mass:**
- The decrease in mass from the original atomic weight is:
\[ \text{Decrease in mass} = \text{Original mass} - \text{New mass} = 12 \text{ amu} - 10.5 \text{ amu} = 1.5 \text{ amu} \]

7. **Calculate the Percentage Decrease:**
- The percentage decrease in mass is calculated as:
\[ \text{Percentage decrease} = \left( \frac{\text{Decrease in mass}}{\text{Original mass}} \right) \times 100 = \left( \frac{1.5 \text{ amu}}{12 \text{ amu}} \right) \times 100 = 12.5\% \]

### Final Answer:
The atomic weight of the carbon atom \(C_6^{12}\) with the modified masses is decreased by **12.5%**.