Earth has a mass of 5.98 × 1024 kg. The average mass of the atoms that make up Earth is 40 u. How many atoms are there in Earth?
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Ans is 9 multiply 10 to the power 49
atomsnumber=5.98E24/massoneatom
If ME is the mass of Earth, m is the average mass of an atom in Earth, and N is the number of atoms, then
ME = N · m or N = ME/m.
Thus,
N =ME/m= (5.98 × 10^24kg) / ((40u)(1.661 × 10^−27kg/u)) = 9.0 × 10^49
To find the number of atoms in Earth, we need to use the following steps:
Step 1: Determine the mass of one atom
The average mass of the atoms that make up Earth is given as 40 u (atomic mass units).
Step 2: Convert the mass of one atom to kilograms
To convert atomic mass units (u) to kilograms (kg), we need to know the value of 1 atomic mass unit in kilograms. This can be found using the fact that 1 u is approximately equal to 1.66 × 10^-27 kg.
Mass of one atom in kg = 40 u × (1.66 × 10^-27 kg/u)
Step 3: Calculate the number of atoms in Earth
To find the number of atoms, we divide the total mass of Earth (5.98 × 10^24 kg) by the mass of one atom in kg.
Number of atoms = (Mass of Earth in kg) / (Mass of one atom in kg)
Now let's plug in the values and calculate:
Mass of one atom in kg = 40 u × (1.66 × 10^-27 kg/u)
= 66.4 × 10^-27 kg
Number of atoms = (5.98 × 10^24 kg) / (66.4 × 10^-27 kg)
After dividing these values, we get the total number of atoms present in Earth.