1 atom of an element weighs `1.792xx10^(-22)g` . The atomic mass of the element is

Options

A. 1.192
B. 17.92
C. 64
D. 108

Answer

To find the atomic mass of the element given the weight of a single atom, we can follow these steps:

### Step 1: Understand the relationship between atomic mass and weight of an atom
The atomic mass of an element (in grams per mole) can be calculated using the weight of a single atom. The relationship is given by Avogadro's number, which is approximately \(6.022 \times 10^{23}\) atoms per mole.

### Step 2: Use the formula to calculate atomic mass
The formula to calculate the atomic mass (M) from the weight of a single atom (w) is:
\[ M = w \times N_A \]
where \(N_A\) is Avogadro's number.

### Step 3: Substitute the values
Given:
- Weight of one atom, \(w = 1.792 \times 10^{-22} \, \text{g}\)
- Avogadro's number, \(N_A = 6.022 \times 10^{23} \, \text{atoms/mole}\)

Now substituting these values into the formula:
\[ M = (1.792 \times 10^{-22} \, \text{g}) \times (6.022 \times 10^{23} \, \text{atoms/mole}) \]

### Step 4: Perform the calculation
Calculating the multiplication:
\[ M = 1.792 \times 6.022 \times 10^{-22 + 23} \]
\[ M = 1.792 \times 6.022 \times 10^{1} \]
\[ M = 1.792 \times 6.022 \times 10^{1} \approx 10.78 \, \text{g/mole} \]

### Step 5: Conclusion
The atomic mass of the element is approximately \(10.78 \, \text{g/mole}\).

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