The Question is from neet-physics , and it was created by the author P.NARASIMHA

Question

Assuming the mass of Earth as $6.64 	imes {10^{24}}kg$ and the average mass of the atoms that make up earth as 40u (atomic mass unit), the number of atoms in the Earth are approximately

P.NARASIMHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: C
## CONCEPT FRAMEWORK
	**Primary Concept**: Mole concept and unit conversion
	**Related Topics**: Atomic mass unit, Avogadro's number
	**Prerequisites**: Understanding of atomic mass unit (amu or u), mole concept, and Avogadro's number.
## SOLUTION PATHWAY
**Given Information**:
	Mass of Earth (M): $6.64 	imes 10^{24}$ kg
	Average mass of atom (m): 40 u
	1 u = $1.66 	imes 10^{-27}$ kg
**Method & Steps**:
	1. Convert the average mass of an atom from atomic mass units (u) to kilograms (kg).
		Reasoning: We need to work with consistent units to calculate the number of atoms.
		Formula/Rule: $1 u = 1.66 	imes 10^{-27} kg$
	2. Calculate the mass of one atom in kg.
		Working: $40 u 	imes 1.66 	imes 10^{-27} kg/u = 6.64 	imes 10^{-26}$ kg/atom
	3. Calculate the number of atoms by dividing the total mass of Earth by the mass of one atom.
		Reasoning: Total Mass / Mass per atom = Number of atoms
		Working: $\frac{6.64 	imes 10^{24} kg}{6.64 	imes 10^{-26} kg/atom} = 10^{50}$ atoms
		Result: Approximately $10^{50}$ atoms
		Verification: The calculation is consistent with the given values.
 ## OPTION ANALYSIS
[A] :x: Incorrect. This is a significantly lower number of atoms than expected.
[B] :x: Incorrect. This is a lower number of atoms than expected.
[C] ✓: Correct. This is the result of the calculation.
[D] :x: Incorrect. This is a significantly higher number of atoms than expected.
 ## LEARNING AIDS
	**Common Mistakes**:
		1. **Unit Conversion Errors**: Forgetting to convert atomic mass units to kilograms can lead to incorrect answers.
			How to avoid: Always ensure all values are in the same units before calculation.
		2. **Incorrect Division**: Dividing mass per atom by the total mass will give the inverse of what's needed.
			How to avoid: Clearly define which quantity represents the total and the per-unit value.
	**Quick Tips**:
		1. **Approximation**: Since the question asks for an approximate value, you can round the numbers to get an estimate quickly.
		2. **Scientific Notation**: Working with scientific notation is essential for problems involving very large or very small numbers.

P.NARASIMHA · Answer

${10^{30}}$

P.NARASIMHA · Answer

${10^{40}}$

P.NARASIMHA · Answer

The correct Option is "${10^{50}}$"

P.NARASIMHA · Answer

${10^{60}}$

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