52 u of He contains

Options

A. `4xx6.022xx10^(23)` atoms
B. 13 atoms
C. `13xx6.022xx10^(23)` atoms
D. 4 atoms

Explanation

To find out how many atoms are present in 52 atomic mass units (u) of Helium (He), we can follow these steps:

### Step 1: Understand the relationship between atomic mass and grams
The atomic mass of Helium is approximately 4 u. This means that 1 mole of Helium (which weighs 4 grams) contains Avogadro's number of atoms, which is approximately \(6.022 \times 10^{23}\) atoms.

### Step 2: Set up the proportion
Since 4 grams of Helium contains \(6.022 \times 10^{23}\) atoms, we can set up a proportion to find out how many atoms are in 52 u of Helium.

### Step 3: Use the formula
Using the relationship:
\[ \text{Number of atoms} = \left(\frac{\text{Atomic mass in u}}{\text{Molar mass in g/mol}}\right) \times \text{Avogadro's number} \]
Substituting the values we have:
\[ \text{Number of atoms} = \left(\frac{52 \, \text{u}}{4 \, \text{g/mol}}\right) \times 6.022 \times 10^{23} \, \text{atoms/mol} \]

### Step 4: Calculate the number of moles
Calculating the number of moles:
\[ \frac{52}{4} = 13 \, \text{moles} \]

### Step 5: Calculate the total number of atoms
Now, multiply the number of moles by Avogadro's number:
\[ \text{Number of atoms} = 13 \times 6.022 \times 10^{23} \, \text{atoms} \]

### Step 6: Final answer
Thus, the total number of atoms in 52 u of Helium is:
\[ \text{Number of atoms} \approx 7.828 \times 10^{24} \, \text{atoms} \]

### Summary
In conclusion, 52 u of Helium contains approximately \(7.828 \times 10^{24}\) atoms.

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