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 approximate number of atoms in the Earth, we can 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 u (atomic mass unit)

### Step 2: Convert the atomic mass unit to kilograms
1 atomic mass unit (u) is approximately \(1.67 \times 10^{-27}\) kg. Therefore, we can convert the average mass of an atom:
\[ m = 40 \, \text{u} = 40 \times 1.67 \times 10^{-27} \, \text{kg} \]
Calculating this gives:
\[ m = 40 \times 1.67 \times 10^{-27} = 6.68 \times 10^{-26} \, \text{kg} \]

### Step 3: Calculate the number of atoms (N)
The number of atoms 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 4: Perform the calculation
Calculating \(N\):
\[ N \approx \frac{6.64 \times 10^{24}}{6.68 \times 10^{-26}} \approx 9.93 \times 10^{49} \]

### Conclusion
The approximate number of atoms in the Earth is \(N \approx 9.93 \times 10^{49}\).

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