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 with two isotopes, we can follow these steps:

### Step 1: Identify the isotopes and their respective atomic weights and abundances.
- Isotope 1: Atomic weight = 85, Relative abundance = 75%
- Isotope 2: Atomic weight = 87, Relative abundance = 25%

### Step 2: Convert the relative abundances from percentages to decimals.
- For Isotope 1: 75% = 0.75
- For Isotope 2: 25% = 0.25

### Step 3: Use the formula for average atomic weight.
The formula for calculating the average atomic weight (AW) is:
\[ AW = (weight_1 \times abundance_1) + (weight_2 \times abundance_2) \]

### Step 4: Substitute the values into the formula.
Substituting the values we have:
\[ AW = (85 \times 0.75) + (87 \times 0.25) \]

### Step 5: Calculate each term.
- For Isotope 1:
\[ 85 \times 0.75 = 63.75 \]
- For Isotope 2:
\[ 87 \times 0.25 = 21.75 \]

### Step 6: Add the results from Step 5.
\[ AW = 63.75 + 21.75 = 85.5 \]

### Step 7: State the average atomic weight.
The average atomic weight of the element is **85.5**.

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