Mass of one atom of an element is 3.64×`10^(−24)`g. This is equal to :

Options

A. 2u
B. 1u
C. 21u
D. 0.12u

Explanation

To solve the problem of finding the mass of one mole of atoms given the mass of one atom, we can follow these steps:

### Step 1: Understand the relationship between mass of one atom and mass of one mole of atoms
The mass of one mole of atoms (in grams) can be calculated using the formula:
\[ \text{Mass of one mole of atoms} = \text{Mass of one atom} \times \text{Avogadro's number} \]
Where Avogadro's number (NA) is approximately \(6.02 \times 10^{23}\) atoms/mole.

### Step 2: Substitute the given values into the formula
Given that the mass of one atom is \(3.64 \times 10^{-24}\) g, we can substitute this value along with Avogadro's number into the formula:
\[ \text{Mass of one mole of atoms} = (3.64 \times 10^{-24} \, \text{g}) \times (6.02 \times 10^{23} \, \text{atoms/mole}) \]

### Step 3: Perform the multiplication
Now, we will multiply the two values:
\[ \text{Mass of one mole of atoms} = 3.64 \times 6.02 \times 10^{-24} \times 10^{23} \]
Calculating \(3.64 \times 6.02\):
\[ 3.64 \times 6.02 \approx 21.9 \]
Now, combining the powers of ten:
\[ 10^{-24} \times 10^{23} = 10^{-1} \]
So, we have:
\[ \text{Mass of one mole of atoms} = 21.9 \times 10^{-1} \, \text{g} = 2.19 \, \text{g} \]

### Step 4: Conclusion
The mass of one mole of the element is approximately \(2.19 \, \text{g}\).

### Final Answer
The mass of one atom of the element, given as \(3.64 \times 10^{-24}\) g, is equal to \(2.19 \, \text{g}\) for one mole of atoms.

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