The relative abundance of two isotopes of an element with atomic weight 85 and 87 is 75% and 25% respectively. Then calculate the average atomic weight of element

Options

A. `86.0`
B. `85.5`
C. `75.5`
D. `40.0`

Answer

To calculate the average atomic weight of the element based on the relative abundance of its isotopes, we can follow these steps:

### Step 1: Identify the isotopes and their atomic weights
We have two isotopes:
- Isotope 1 (M1) with an atomic weight of 85
- Isotope 2 (M2) with an atomic weight of 87

### Step 2: Identify the relative abundances
The relative abundances are given as:
- Isotope 1 (x1) = 75% = 0.75
- Isotope 2 (x2) = 25% = 0.25

### Step 3: Use the formula for average atomic weight
The formula to calculate the average atomic weight (A_avg) is:
\[ A_{avg} = \frac{(M_1 \cdot x_1) + (M_2 \cdot x_2)}{x_1 + x_2} \]

### Step 4: Substitute the values into the formula
Substituting the values we have:
\[ A_{avg} = \frac{(85 \cdot 0.75) + (87 \cdot 0.25)}{0.75 + 0.25} \]

### Step 5: Calculate the numerator
Calculating the products:
- \(85 \cdot 0.75 = 63.75\)
- \(87 \cdot 0.25 = 21.75\)

Now, add these two results:
\[ 63.75 + 21.75 = 85.5 \]

### Step 6: Calculate the denominator
The denominator is:
\[ 0.75 + 0.25 = 1 \]

### Step 7: Final calculation
Now, substitute back into the formula:
\[ A_{avg} = \frac{85.5}{1} = 85.5 \]

### Conclusion
The average atomic weight of the element is **85.5**.

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