Each element has a characteristic atomic mass. The atoms are extremely small particles and it is very difficult to determine their actual masses. For example, mass of one atom of hydrogen has been found to be `1.66 xx 10^(-24)` . Obviously, such a small mass cannot be determined even with the help of a very sensitive balance. To overcome, this problem, the atomic masses are expressed as relative masses i.e., with reference to mass of a standard atom. In 1961, the International Union of Chemists selected the stable isotope of carbon ( carbon -12) as the standard for comparing the atomic and molecular masses of elements and compounds. The atomic mass of the standard, the isotope carbon-12 of carbon is chosen to be 12. Thus, atomic mass may be defined as the relative mass of an atom of the element as compared to an atom of carbon ( carbon-12) taken as 12.
52u of He contains

Options

A. `4 xx 6.022 xx 10^(23)` atoms
B. 13 atoms
C. `13 xx 6.022 xx 10^(23)` atoms
D. 4 atoms

Explanation

To solve the problem of how many atoms are contained in 52 amu (atomic mass units) of helium (He), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Molar Mass of Helium**:
The molar mass of helium (He) is approximately 4 g/mol. This means that one mole of helium weighs 4 grams.

2. **Convert Atomic Mass Units to Grams**:
Since we are given the mass in atomic mass units (amu), we need to convert this to grams to find the number of moles. The conversion factor is that 1 amu is equivalent to \(1.66 \times 10^{-24}\) grams. However, since we are dealing with moles, we can directly use the molar mass.

3. **Calculate the Number of Moles**:
To find the number of moles of helium in 52 amu, we use the formula:
\[ \text{Number of moles} = \frac{\text{Mass (in grams)}}{\text{Molar mass (g/mol)}} \]
Since 52 amu is equivalent to 52 grams (for the sake of this calculation, we are assuming the mass is in grams), we can calculate:
\[ \text{Number of moles} = \frac{52 \text{ g}}{4 \text{ g/mol}} = 13 \text{ moles} \]

4. **Use Avogadro's Number to Find the Number of Atoms**:
Avogadro's number (\(N_A\)) is \(6.022 \times 10^{23}\) atoms/mole. To find the total number of atoms in 13 moles of helium, we multiply the number of moles by Avogadro's number:
\[ \text{Number of atoms} = 13 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole} \]
\[ \text{Number of atoms} = 7.98 \times 10^{24} \text{ atoms} \]

### Final Answer:
Thus, 52 amu of helium contains approximately \(7.98 \times 10^{24}\) atoms.

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