Question

The atomic weight of silver is 107.868 amu. Naturally occurring silver consists of two isotopes. 107Ag (mass = 106.904 amu) and 109Ag (mass = 108.905 amu). What percentage of naturally occurring silver is the heavier isotope? a. 45.4% b. 52.6% c. 62.7% d. 48.2% e. 51.7%

Answer 1

The heavier isotope is 48.2 % (option d)

Step-by-step explanation:

Step 1: Data given

Atomic weight of silver = 107.868 amu

Isotopes of silver:

107Ag = 106.904 amu

109Ag = 108.905 amu

Step 2: Calculate the percentages

107.868 = 106.904 * x + 108.905 *y

x+y = 1 ⇒ x = 1 - y

107.868 = 106.904 (1 - y) + 108.905*y

107.868 = 106.904 - 106.904y + 108.905y

0.964 = 2.001y

y = 0.4818

x = 1 - 0.4818 = 0.5182

Percentage 109Ag = 48.18 %

Percentage 107Ag = 51.82 %

The heavier isotope is 109Ag. Its percentage is 48.18 ≈ 48.2 %