If `1//6`, in place of `1//12`, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will:

Options

A. Decrease twice
B. Increase two folds
C. Remain uncharges
D. Be a function of the molecular mass of element

Explanation

To solve the question, we need to understand how the mass of one mole of a substance is calculated and how changing the reference for the atomic mass unit affects this calculation.

### Step-by-Step Solution:

1. **Understanding Atomic Mass Unit (AMU)**:
- The atomic mass unit (AMU) is defined based on the mass of a carbon-12 atom. Specifically, 1 AMU is equal to 1/12th the mass of a carbon-12 atom.

2. **Changing the Reference**:
- The question states that instead of using 1/12, we are using 1/6. This means that we are redefining the atomic mass unit such that 1 AMU now corresponds to 1/6th the mass of a carbon atom.

3. **Calculating the New AMU**:
- If 1 AMU is now defined as 1/6 of the mass of a carbon atom, then the mass of a carbon atom in AMU terms is now doubled. This is because the original definition (1/12) was half of the new definition (1/6).
- Therefore, if 1 AMU = 1/6 of the carbon atom, then 1 carbon atom = 2 AMU.

4. **Understanding Avogadro's Number**:
- Avogadro's number (Na) is the number of atoms in one mole of a substance, which is approximately \(6.022 \times 10^{23}\).
- The mass of one mole of a substance can be calculated using the formula:
\[ \text{Mass of 1 mole of substance} = \text{Na} \times \text{AMU} \]

5. **Calculating the Mass of One Mole with New AMU**:
- In the original system, if we consider the mass of carbon as 12 g for 1 mole, then:
\[ \text{Mass of 1 mole} = \text{Na} \times 1 \text{ AMU} = \text{Na} \times 1 \text{ (1/12 of carbon)} \]
- In the new system, with 1 AMU now being 2 (since it corresponds to 1/6 of carbon):
\[ \text{Mass of 1 mole} = \text{Na} \times 2 \text{ AMU} = \text{Na} \times 2 \text{ (1/6 of carbon)} \]

6. **Conclusion**:
- When we substitute the new AMU into the mass calculation, we find that:
\[ \text{Mass of 1 mole} = \text{Na} \times 2 \text{ AMU} = \text{Na} \times 1 \text{ AMU} \text{ (original system)} \]
- Therefore, the mass of one mole of a substance remains unchanged despite the change in the definition of AMU.

### Final Answer:
The mass of one mole of a substance will **remain unchanged**.