Answer :
The percentage occurrence of M50 is 15%, while M52 has an 85% natural abundance. This is derived using the weighted average formula for calculating average atomic mass and solving for the unknown percentage.
To calculate the percentage occurrence of two isotopes of element M, we use the concept that the average atomic weight is a weighted average of the isotopes' masses according to their abundance. Let's denote the percentage of M50 as x and the percentage of M52 as 100-x, since the total must add up to 100%. The average atomic weight, 51.7 amu, is given by the equation:
51.7 = (50 imes x/100) + (52 imes (100-x)/100)
To solve for x, multiply through by 100 and collect like terms:
5170 = 50x + 5200 - 52x
Combining the x terms and moving the constants to the other side yields:
2x = 5200 - 5170
x = 30/2
x = 15
Thus, M50 has a 15% abundance and M52 has an 85% abundance. To check, we can put these values back into the average atomic weight equation:
51.7 = (50 imes 0.15) + (52 imes 0.85)
51.7 = 7.5 + 44.2
51.7 = 51.7
This confirms the correct percentages of isotopic abundance for element M.
