Question

The average atomic mass of all naturally occurring lithium atoms is 6.941 amu. the two isotopes of lithium are lithium-6 and lithium-7. are these isotopes equally common? if not, which is more plentiful in nature, and how do you know?

Answer 1

No, the two isotopes of lithium-6 and lithium-7 are not equally common.  
The more plentiful isotope would be lithium-7. 
This can be easily demonstrated by assuming that both isotopes were equally common. If that were the case, the average atomic mass would be (6 + 7)/2 = 6.5 amu. Now compare that value if they were both equal to the actual value found in nature. The value found in nature is 6.941 amu which is heavier than the 6.5 amu that would happen if they were equally common. Since the natural value is heavier, that means that there has to be more of the heavier isotope than there is of the lighter one. Therefore lithium-7 is more common than lithium-6.