Assuming the mass of the earth as `6.64xx10^(24)`kg Kg and the average mass of the atoms that make up the earth as 40 u ( atomic mass. Unit ) , the number of atoms in the earth is approximately

Options

A. `10^(30)`
B. `10^(40)`
C. `10^(50)`
D. `10^(60)`

Answer

To find the number of atoms in the Earth, we will follow these steps:

### Step 1: Understand the given data
- Mass of the Earth, \( M = 6.64 \times 10^{24} \) kg
- Average mass of an atom, \( m = 40 \, \text{u} \)

### Step 2: Convert atomic mass units (u) to kilograms
1 atomic mass unit (u) is approximately \( 1.67 \times 10^{-27} \) kg. Therefore, the mass of one atom in kilograms is:
\[ m = 40 \, \text{u} = 40 \times 1.67 \times 10^{-27} \, \text{kg} \]

### Step 3: Calculate the mass of one atom
\[ m = 40 \times 1.67 \times 10^{-27} = 6.68 \times 10^{-26} \, \text{kg} \]

### Step 4: Calculate the number of atoms in the Earth
The number of atoms \( N \) can be calculated using the formula:
\[ N = \frac{M}{m} \]
Substituting the values we have:
\[ N = \frac{6.64 \times 10^{24} \, \text{kg}}{6.68 \times 10^{-26} \, \text{kg}} \]

### Step 5: Perform the division
\[ N = \frac{6.64}{6.68} \times 10^{24 + 26} = \frac{6.64}{6.68} \times 10^{50} \]

### Step 6: Simplify the fraction
Calculating \( \frac{6.64}{6.68} \) gives approximately \( 0.993 \). Therefore:
\[ N \approx 0.993 \times 10^{50} \approx 10^{50} \, \text{atoms} \]

### Conclusion
The approximate number of atoms in the Earth is \( \approx 10^{50} \).

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