A sample of sodium has a mass of `46g.` What is the mass of the same number of calcium atoms as sodium atoms present in given sample ?

Options

A. 20gm
B. 40gm
C. 60gm
D. 80gm

Answer

To find the mass of the same number of calcium atoms as sodium atoms present in a given sample, we will follow these steps:

### Step 1: Calculate the number of moles of sodium
The mass of sodium given is 46 grams. The molar mass of sodium (Na) is approximately 23 g/mol.

\[ \text{Number of moles of Na} = \frac{\text{mass of Na}}{\text{molar mass of Na}} = \frac{46 \, \text{g}}{23 \, \text{g/mol}} = 2 \, \text{moles} \]

### Step 2: Calculate the number of sodium atoms
Using Avogadro's number, which is \(6.022 \times 10^{23}\) atoms/mole, we can find the total number of sodium atoms.

\[ \text{Number of Na atoms} = \text{moles of Na} \times \text{Avogadro's number} = 2 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mole} = 1.2044 \times 10^{24} \, \text{atoms} \]

### Step 3: Determine the number of calcium atoms
Since we need the same number of calcium atoms as sodium atoms, the number of calcium atoms will also be \(1.2044 \times 10^{24}\) atoms.

### Step 4: Calculate the mass of calcium
The molar mass of calcium (Ca) is approximately 40 g/mol. To find the mass of the same number of calcium atoms, we first convert the number of calcium atoms back to moles.

\[ \text{Number of moles of Ca} = \frac{\text{Number of Ca atoms}}{\text{Avogadro's number}} = \frac{1.2044 \times 10^{24} \, \text{atoms}}{6.022 \times 10^{23} \, \text{atoms/mole}} \approx 2 \, \text{moles} \]

Now, we can find the mass of calcium:

\[ \text{Mass of Ca} = \text{Number of moles of Ca} \times \text{molar mass of Ca} = 2 \, \text{moles} \times 40 \, \text{g/mol} = 80 \, \text{g} \]

### Final Answer
The mass of the same number of calcium atoms as sodium atoms present in the given sample is **80 grams**.

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