In chemistry, 'mole' is an essential tool for the chemical calculations. It is a basic SI unit adopted by the `14^(th)` general conference on weights and measurements in 1971. A mole contains as many elementary particles as the number of atoms present in 12 g of `""^(12)C` . 1 mole of a gas at STP occupies 22.4 litre volume. Molar volume of solids and liquids is not definite. Molar mass of a substance is also called gram-atomic mass or gram molecular mass. The virtual meaning of mole is plenty, heap or the collection of large numbers. 1 mole of a substance contains `6.022 xx 10^(23)` elementary particles like atom or molecule. Atomic mass unit (amu) is the unit of atomic mass, e.g., atomic mass of single carbon is 12 amu.
The mass of 1 amu is approximately

Options

A. 1 g
B. `0.5g`
C. `1.66xx10^(-24)g`
D. `3.2xx10^(-24)g`

Explanation

To find the approximate mass of one atomic mass unit (AMU), we can follow these steps:

### Step 1: Understand the Definition of AMU
AMU (Atomic Mass Unit) is defined as 1/12th the mass of a carbon-12 atom. This means that if we know the mass of a carbon-12 atom, we can calculate the mass of 1 AMU.

### Step 2: Know the Molar Mass of Carbon-12
The molar mass of carbon-12 is 12 grams. This means that 12 grams of carbon-12 contains Avogadro's number of atoms, which is approximately \(6.022 \times 10^{23}\) atoms.

### Step 3: Calculate the Mass of One Carbon Atom
To find the mass of one carbon atom, we divide the total mass of 12 grams by the number of atoms in that mass:
\[ \text{Mass of one carbon atom} = \frac{12 \text{ grams}}{6.022 \times 10^{23} \text{ atoms}} \]

### Step 4: Calculate the Mass of One AMU
Since 1 AMU is defined as 1/12th the mass of a carbon-12 atom, we can calculate it as follows:
\[ \text{Mass of 1 AMU} = \frac{1}{12} \times \left(\frac{12 \text{ grams}}{6.022 \times 10^{23} \text{ atoms}}\right) \]

### Step 5: Simplify the Calculation
This simplifies to:
\[ \text{Mass of 1 AMU} = \frac{12 \text{ grams}}{12 \times 6.022 \times 10^{23}} = \frac{1}{6.022 \times 10^{23}} \text{ grams} \]

### Step 6: Final Calculation
Calculating this gives:
\[ \text{Mass of 1 AMU} \approx 1.66 \times 10^{-24} \text{ grams} \]

### Conclusion
Thus, the approximate mass of one atomic mass unit (AMU) is \(1.66 \times 10^{-24}\) grams.

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