An atom of an element weighs `6.644 times 10^(-23)` g. Calculate g atoms of element in 40 kg-

Options

A. 10 gm atom
B. 100 gm atom
C. 1000 gm atom
D. `10^(4)` gm atom

Explanation

To solve the problem step by step, we will follow the outlined procedure in the video transcript.

### Step 1: Understand the Given Data
We are given:
- Weight of one atom of the element = \(6.644 \times 10^{-23}\) g
- Total mass of the element = 40 kg

### Step 2: Convert the Total Mass to Grams
Since the weight of the atom is given in grams, we need to convert the total mass from kilograms to grams.

\[ 40 \text{ kg} = 40 \times 1000 \text{ g} = 40000 \text{ g} \]

### Step 3: Calculate the Molecular Mass of the Element
To find the molecular mass, we will use the relationship between the weight of one atom and Avogadro's number. The formula for molecular mass (M) can be derived as follows:

\[ M = \text{Weight of one atom} \times N_A \]

Where \(N_A\) (Avogadro's number) is approximately \(6.022 \times 10^{23}\) atoms/mol.

Substituting the values:

\[ M = (6.644 \times 10^{-23} \text{ g}) \times (6.022 \times 10^{23} \text{ atoms/mol}) \]

Calculating this gives:

\[ M = 40 \text{ g/mol} \]

### Step 4: Calculate the Number of Moles
Now, we can calculate the number of moles (n) using the formula:

\[ n = \frac{\text{Given mass}}{\text{Molecular mass}} \]

Substituting the values:

\[ n = \frac{40000 \text{ g}}{40 \text{ g/mol}} = 1000 \text{ moles} \]

### Step 5: Conclusion
The number of gram atoms of the element in 40 kg is 1000.

### Final Answer
The number of gram atoms in 40 kg of the element is **1000 gram atoms**.

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