Let the mass of electron is two times, mass of proton is `1/4^(th)` and mass of neutron is 3/2 of original mass. Then, the atomic weight of `6^(C^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-12 atom given the modified masses of the particles (protons, neutrons, and electrons).

### Step-by-Step Solution:

1. **Identify the Original Masses:**
- The original mass of a proton (m_p) is approximately 1 amu.
- The original mass of a neutron (m_n) is approximately 1 amu.
- The original mass of an electron (m_e) is negligible (approximately 0.0005 amu).

2. **Modified Masses:**
- According to the problem:
- Mass of electron = 2 * original mass of proton = 2 * 1 amu = 2 amu.
- Mass of proton = 1/4 * original mass of proton = 1/4 * 1 amu = 0.25 amu.
- Mass of neutron = 3/2 * original mass of neutron = 3/2 * 1 amu = 1.5 amu.

3. **Calculate Total Mass of Carbon-12:**
- Carbon-12 has 6 protons and 6 neutrons.
- Total mass from protons = 6 * mass of proton = 6 * 0.25 amu = 1.5 amu.
- Total mass from neutrons = 6 * mass of neutron = 6 * 1.5 amu = 9 amu.
- Total atomic mass of Carbon-12 = Total mass from protons + Total mass from neutrons = 1.5 amu + 9 amu = 10.5 amu.

4. **Calculate the Decrease in Mass:**
- Original atomic mass of Carbon-12 = 12 amu.
- Decrease in mass = Original mass - New mass = 12 amu - 10.5 amu = 1.5 amu.

5. **Calculate Percentage Decrease:**
- Percentage decrease = (Decrease in mass / Original mass) * 100
- Percentage decrease = (1.5 amu / 12 amu) * 100 = 12.5%.

### Final Answer:
The atomic weight of the modified Carbon-12 atom is 10.5 amu, and the percentage decrease in mass is 12.5%.