To answer the given question, we need to determine how many times greater the mass of the Earth is compared to the mass of a hydrogen atom. Let's go through the detailed, step-by-step solution.
### Step 1: Understand the given data
- Mass of a hydrogen atom [tex]\( m_H \)[/tex] = [tex]\( 1.67 \times 10^{-27} \)[/tex] kg
- Mass of the Earth [tex]\( m_E \)[/tex] = [tex]\( 5.972 \times 10^{24} \)[/tex] kg
- Mass of the globe model of the Earth [tex]\( m_{globe} \)[/tex] = 829 kg
### Step 2: Calculate the mass ratio
To find out how many times greater the mass of the Earth is compared to the mass of a hydrogen atom, we use the following formula:
[tex]\[
\text{Mass ratio} = \frac{\text{Mass of the Earth}}{\text{Mass of a hydrogen atom}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Mass ratio} = \frac{5.972 \times 10^{24}}{1.67 \times 10^{-27}}
\][/tex]
### Step 3: Perform the division
When dividing numbers in scientific notation, we divide the coefficients and subtract the exponents of 10:
[tex]\[
\text{Mass ratio} = \frac{5.972}{1.67} \times 10^{24 - (-27)}
\][/tex]
First, calculate the division of the coefficients:
[tex]\[
\frac{5.972}{1.67} \approx 3.576
\][/tex]
Next, calculate the exponents:
[tex]\[
10^{24 - (-27)} = 10^{24 + 27} = 10^{51}
\][/tex]
Combining these results:
[tex]\[
\text{Mass ratio} \approx 3.576 \times 10^{51}
\][/tex]
### Step 4: Interpretation of the results
The mass of the Earth is approximately [tex]\( 3.576 \times 10^{51} \)[/tex] times greater than the mass of a hydrogen atom.
### Step 5: Additional information
The mass of the globe model of the Earth is provided for context, but it does not affect the calculation of the mass ratio between the Earth and a hydrogen atom.
### Summary
- The mass of a hydrogen atom is [tex]\( 1.67 \times 10^{-27} \)[/tex] kg.
- The mass of the Earth is [tex]\( 5.972 \times 10^{24} \)[/tex] kg.
- The mass of the Earth is approximately [tex]\( 3.576 \times 10^{51} \)[/tex] times greater than the mass of a hydrogen atom.
- The mass of the globe model is 829 kg, which is additional context but not directly related to the calculated mass ratio.
This detailed step-by-step solution demonstrates the calculation and provides a clear interpretation of the results.
