How many uranium atoms are there in 8.2 g
of pure uranium? The mass of one uranium
atom is 4 × 10^−26 kg.
First, we need to convert the mass of uranium from grams to kilograms:
8.2 g * (1 kg / 1000 g) = 0.0082 kg
Now we'll divide the total mass of uranium by the mass of a single uranium atom to find the number of atoms:
0.0082 kg / (4 × 10^−26 kg/atom) = 2.05 × 10^24 atoms
So there are approximately 2.05 × 10^24 uranium atoms in 8.2g of pure uranium.
To find the number of uranium atoms in 8.2 g of pure uranium, we can use the following steps:
Step 1: Convert the mass of one uranium atom to grams.
Given: Mass of one uranium atom = 4 × 10^−26 kg
1 kg = 1000 g, so the mass of one uranium atom in grams is
= (4 × 10^−26) kg × (1000 g/1 kg)
= 4 × 10^−23 g
Step 2: Calculate the number of uranium atoms in 8.2 g of pure uranium.
The number of atoms (n) can be calculated using Avogadro's number (6.022 × 10^23 atoms/mol) and the molar mass of uranium (238.03 g/mol). We use the following equation:
n = (mass of uranium in grams) / (molar mass of uranium in grams)
n = 8.2 g / 238.03 g/mol
Calculating n:
n = 8.2 g / 238.03 g/mol
n = 0.034 ft8.2/ 238.03
n ≈ 0.0344 mol
Step 3: Convert the number of moles to the number of atoms.
To convert from moles to atoms, we multiply the number of moles by Avogadro's number (6.022 × 10^23 atoms/mol).
Number of atoms = (0.0344 mol) × (6.022 × 10^23 atoms/mol)
Number of atoms ≈ 2.073 × 10^22
Therefore, there are approximately 2.073 × 10^22 uranium atoms in 8.2 g of pure uranium.
To find out the number of uranium atoms in 8.2 g of pure uranium, we need to use the concept of molar mass and Avogadro's number.
1. Determine the molar mass of uranium: The atomic mass of uranium is approximately 238 atomic mass units (u). Therefore, the molar mass of uranium can be calculated by multiplying this atomic mass by the molar mass constant (1 g/mol), which gives us 238 g/mol.
2. Calculate the number of moles of uranium: Divide the given mass (8.2 g) by the molar mass of uranium (238 g/mol) to get the number of moles. So, 8.2 g / 238 g/mol = 0.0345 mol.
3. Use Avogadro's number to find the number of atoms: Avogadro's number (6.022 × 10^23) represents the number of atoms or molecules in one mole of any substance. Multiply the number of moles (0.0345 mol) by Avogadro's number to get the number of uranium atoms. Thus, 0.0345 mol × 6.022 × 10^23 atoms/mol = 2.08 × 10^22 uranium atoms.
Therefore, there are approximately 2.08 × 10^22 uranium atoms in 8.2 g of pure uranium.