Final answer:
To calculate the average atomic mass for an element with three naturally occurring isotopes, multiply the mass of each isotope by its abundance and sum up the results. The most likely average atomic mass for this element with isotopes X-413, X-415, and X-416, and abundance of 62%, 24%, and 14% respectively, is 413 amu.
Step-by-step explanation:
To calculate the average atomic mass for an element with three naturally occurring isotopes, you need to multiply the mass of each isotope by its respective abundance and then sum up the results. In this case, we have three isotopes X-413, X-415, and X-416 with natural abundances of 62%, 24%, and 14%, respectively. The most likely average atomic mass for this element can be calculated as follows:
- Mass of X-413 = 413 amu * 0.62 = 255.06 amu
- Mass of X-415 = 415 amu * 0.24 = 99.60 amu
- Mass of X-416 = 416 amu * 0.14 = 58.24 amu
- Average atomic mass = 255.06 amu + 99.60 amu + 58.24 amu = 413.9 amu
Therefore, the most likely average atomic mass for this element is 413 amu (Option A).
The most likely average atomic mass for the new element given the stable isotopes and their natural abundances is 414 amu, which is option D after rounding the calculated weighted average of 413.90 amu.
To calculate the most likely average atomic mass for the newly discovered element with stable isotopes X - 413, X - 415, and X - 416, we need to take into account the natural abundances. We do this by multiplying each isotope's mass by its natural abundance (in decimal form) and then summing these products together.
The calculation would look like this:
(256.06 amu) + (99.60 amu) + (58.24 amu)
256.06 amu + 99.60 amu + 58.24 amu = 413.90 amu
After rounding to the nearest whole number, the most likely average atomic mass would be 414 amu, which corresponds to option D.