Final answer:
The false statement is that 'Diamonds are twice as hard as apatite' because the Mohs hardness scale is qualitative and does not represent hardness in quantifiable multiples.
Step-by-step explanation:
The statement that is false regarding the actual hardness of minerals using the Mohs hardness scale is 'b. Diamonds are twice as hard as apatite'.
The Mohs scale of mineral hardness is a qualitative scale, indicating that the numbers on the scale do not represent a proportional increase in hardness. Therefore, a diamond rated at 10 on the Mohs scale is not twice as hard as apatite, which is rated at 5. The Mohs scale simply shows that a mineral with a higher number can scratch those below it, but not how much harder it is in a quantifiable measure.
In reference to the other statements provided, 'a. Your fingernail can scratch a sample of gypsum' is true because a fingernail has a hardness of about 2.5 and gypsum has a hardness of 2. 'c. Diamonds are more than seven times as hard as quartz' is a misleading statement as the Mohs scale does not indicate multiples of hardness between ratings. Lastly, 'd. Quartz will scratch anything made of steel' is generally true as quartz has a hardness of 7 and steel typically falls between 4 and 4.5 on the Mohs scale.