The element silver has an atomic weight of 108 and consists of two stable isotopes silver-107 and silver-109. The isotope silver-107 has a mass of 107 amu and a percent natural abundance of 51.8 % The isotope silver-109 has a percent natural abundance of 48.2 % What is the mass of silver-1092?
The Correct Answer and Explanation is :
To find the mass of silver-109 (( m_{109} )), we use the equation for the weighted average atomic mass:
[
\text{Atomic Weight} = (m_{107} \times f_{107}) + (m_{109} \times f_{109})
]
where:
- ( \text{Atomic Weight} = 108 ) amu
- ( m_{107} = 107 ) amu
- ( f_{107} = 0.518 ) (fractional abundance)
- ( f_{109} = 0.482 ) (fractional abundance)
- ( m_{109} ) is unknown.
Rearrange the equation to solve for ( m_{109} ):
[
108 = (107 \times 0.518) + (m_{109} \times 0.482)
]
[
108 = (55.426) + (m_{109} \times 0.482)
]
[
m_{109} \times 0.482 = 108 – 55.426
]
[
m_{109} \times 0.482 = 52.574
]
[
m_{109} = \frac{52.574}{0.482}
]
[
m_{109} \approx 109.1 \text{ amu}
]
Explanation:
The element silver (Ag) has an atomic weight of 108 amu, which is the weighted average of its two stable isotopes: silver-107 and silver-109. The percentage abundance of silver-107 is 51.8%, and silver-109 is 48.2%. The formula for calculating atomic weight considers the relative abundances and atomic masses of the isotopes.
By substituting the known values, we set up an equation and solve for the unknown mass of silver-109. The result is approximately 109.1 amu, which aligns with the expected atomic structure of silver. This confirms the reliability of our calculation, as the mass is close to the atomic number of the isotope.
Now, I’ll generate an image to visually represent the isotopes of silver.
Here is the image representation of silver (Ag) with its two stable isotopes, Silver-107 and Silver-109. It illustrates their atomic structures, natural abundances, and the atomic weight calculation leading to 108 amu. Let me know if you need any modifications or further explanations!
