`3.011 xx 10^22` atoms of an element weighs `1.15 gm`. The atomic mass of the element is :

Options

A. `10 amu`
B. `2.3 amu`
C. `35.5 amu`
D. `23 amu`

Answer

To find the atomic mass of the element given that \(3.011 \times 10^{22}\) atoms weigh \(1.15 \, \text{g}\), we can follow these steps:

### Step 1: Calculate the mass of one atom
To find the mass of a single atom, we divide the total mass by the number of atoms:

\[ \text{Mass of one atom} = \frac{\text{Total mass}}{\text{Number of atoms}} = \frac{1.15 \, \text{g}}{3.011 \times 10^{22} \, \text{atoms}} \]

### Step 2: Calculate the mass of one mole of atoms
Since one mole of atoms contains \(6.022 \times 10^{23}\) atoms (Avogadro's number), we can find the mass of one mole by multiplying the mass of one atom by Avogadro's number:

\[ \text{Mass of one mole} = \text{Mass of one atom} \times 6.022 \times 10^{23} \]

### Step 3: Substitute and simplify
Substituting the expression from Step 1 into Step 2 gives:

\[ \text{Mass of one mole} = \left(\frac{1.15 \, \text{g}}{3.011 \times 10^{22} \, \text{atoms}}\right) \times 6.022 \times 10^{23} \]

### Step 4: Calculate the final value
Now we can calculate the mass of one mole:

\[ \text{Mass of one mole} = \frac{1.15 \times 6.022}{3.011} \, \text{g} \]

Calculating this gives:

\[ \text{Mass of one mole} \approx \frac{6.9223}{3.011} \approx 2.297 \times 10^{1} \, \text{g} \approx 23 \, \text{g} \]

### Conclusion
Thus, the atomic mass of the element is approximately \(23 \, \text{g/mol}\).

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