The natural uranium consists of three isotopes `""_(92)^(238)U, ""_(92)^(235)U and ""_(92)^(234)U` in the ratio 99.274 : 0.720, 0.006. Find the average atomic mass of uranium.

Answer

To find the average atomic mass of natural uranium consisting of three isotopes, we can follow these steps:

### Step 1: Identify the isotopes and their atomic masses
The isotopes of uranium and their respective atomic masses are:
- \( U^{238}_{92} \) with atomic mass = 238
- \( U^{235}_{92} \) with atomic mass = 235
- \( U^{234}_{92} \) with atomic mass = 234

### Step 2: Identify the ratios of the isotopes
The ratios of the isotopes are given as:
- \( x_1 = 99.274 \) for \( U^{238}_{92} \)
- \( x_2 = 0.720 \) for \( U^{235}_{92} \)
- \( x_3 = 0.006 \) for \( U^{234}_{92} \)

### Step 3: Use the formula for average atomic mass
The formula for calculating the average atomic mass (AAM) is:
\[ \text{AAM} = \frac{(a_1 \cdot x_1) + (a_2 \cdot x_2) + (a_3 \cdot x_3)}{x_1 + x_2 + x_3} \]
Where:
- \( a_1, a_2, a_3 \) are the atomic masses of the isotopes.
- \( x_1, x_2, x_3 \) are the ratios of the isotopes.

### Step 4: Substitute the values into the formula
Substituting the values we identified:
\[ \text{AAM} = \frac{(238 \cdot 99.274) + (235 \cdot 0.720) + (234 \cdot 0.006)}{99.274 + 0.720 + 0.006} \]

### Step 5: Calculate the numerator
Calculating each term in the numerator:
- \( 238 \cdot 99.274 = 23627.212 \)
- \( 235 \cdot 0.720 = 169.2 \)
- \( 234 \cdot 0.006 = 1.404 \)

Now, adding these values together:
\[ 23627.212 + 169.2 + 1.404 = 23897.816 \]

### Step 6: Calculate the denominator
Calculating the denominator:
\[ 99.274 + 0.720 + 0.006 = 100.000 \]

### Step 7: Divide the numerator by the denominator
Now, we can find the average atomic mass:
\[ \text{AAM} = \frac{23897.816}{100.000} = 238.97816 \]

### Step 8: Round the result
Rounding to three decimal places, we get:
\[ \text{Average Atomic Mass of Uranium} \approx 237.978 \]

### Final Answer
The average atomic mass of uranium is approximately **237.978**.

---