If we consider that $$\frac{1}{6}$$, in place of $$\frac{1}{12}$$, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

The relative atomic mass unit (amu) is presently defined as $$1\,\text{amu}=\dfrac{1}{12}\text{(mass of one }{}^{12}C\text{ atom)}$$.

Suppose the community re-defines the atomic mass unit as
$$1\,\text{new amu}=\dfrac{1}{6}\text{(mass of one }{}^{12}C\text{ atom)}.$$

This new unit is exactly twice as heavy as the old one because $$\dfrac{1}{6}$$ is twice $$\dfrac{1}{12}$$. Hence every numerical atomic (or molecular) mass expressed in the new units will become half of its old numerical value. For example:

Old scale: $$\text{H}_2$$ had $$2.016\,\text{amu}.$$
New scale: $$\text{H}_2$$ will be $$1.008\,\text{new amu}.$$

Avogadro’s number, by definition, is chosen so that one mole of carbon-12 weighs exactly $$12\text{ g}$$ on whatever mass scale is adopted. When the size of the atomic mass unit is altered, the number of units needed to make $$12\text{ g}$$ of carbon-12 must change inversely. Specifically, since each new amu is twice as heavy, only half as many of them fit into $$12\text{ g}$$; therefore Avogadro’s number becomes half of its former value.

For any substance, molar mass is calculated as

$$\text{molar mass} = (\text{atomic or molecular mass in amu}) \times (\text{grams per amu}).$$

• The numerical atomic/molecular mass is halved.
• The conversion factor “grams per amu” is doubled (because Avogadro’s number is halved).
Thus the product—and hence the mass of one mole—remains exactly the same.

Therefore, even after redefining the atomic mass unit, the molar mass of every substance is unchanged.

Option C which is: Remain unchanged