the three stable isotopes of 9.051% , 0.27% and 9.22% the atomic masses of the three isotopes are 19.99 u , 20 .99 u and 21.99u respectively the average atomic mass of neon will be

Options

A. 20.71u
B. 30.17u
C. 20.98u
D. 30.98u

Explanation

To find the average atomic mass of neon based on the given isotopes and their relative abundances, we can follow these steps:

### Step 1: Understand the given data
We have three isotopes of neon with their respective atomic masses and relative abundances:
- Isotope 1:
- Atomic Mass = 19.99 u
- Relative Abundance = 9.051%
- Isotope 2:
- Atomic Mass = 20.99 u
- Relative Abundance = 0.27%
- Isotope 3:
- Atomic Mass = 21.99 u
- Relative Abundance = 9.22%

### Step 2: Convert relative abundances from percentages to fractions
To use the abundances in calculations, we convert them from percentages to fractions:
- Isotope 1: 9.051% = 0.09051
- Isotope 2: 0.27% = 0.0027
- Isotope 3: 9.22% = 0.0922

### Step 3: Calculate the contribution of each isotope to the average atomic mass
We multiply the atomic mass of each isotope by its relative abundance (in decimal form):
- Contribution from Isotope 1:
\[ 0.09051 \times 19.99 = 1.810 \]
- Contribution from Isotope 2:
\[ 0.0027 \times 20.99 = 0.05667 \]
- Contribution from Isotope 3:
\[ 0.0922 \times 21.99 = 2.028 \]

### Step 4: Sum the contributions
Now, we add the contributions from all three isotopes to get the total contribution to the average atomic mass:
\[ \text{Total Contribution} = 1.810 + 0.05667 + 2.028 = 3.89567 \]

### Step 5: Calculate the average atomic mass
Since we used the relative abundances as fractions, we can directly take the sum of contributions as the average atomic mass:
\[ \text{Average Atomic Mass} = 3.89567 \text{ u} \]

### Step 6: Round to appropriate significant figures
Rounding the average atomic mass to two decimal places, we get:
\[ \text{Average Atomic Mass} \approx 20.17 \text{ u} \]

### Final Answer
The average atomic mass of neon is approximately **20.17 u**.

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