The Statue of Liberty is made of `2.0 xx 10^(5)` lbs of copper sheets bolted to a framework (1 lb = 454 g) How many atoms of copper are on the statue?
(Atomic weight: Cu = 63.5).

Options

A. `2.1 xx 10^(27)`
B. `8.6 xx 10^(29)`
C. `4.3 xx 10^(26)`
D. `8.6 xx 10^(26)`

Explanation

To find the number of atoms of copper in the Statue of Liberty, we will follow these steps:

### Step 1: Convert pounds to grams
Given that the weight of the Statue of Liberty is \(2.0 \times 10^5\) lbs and knowing that \(1 \text{ lb} = 454 \text{ g}\), we can convert the weight to grams.

\[ \text{Weight in grams} = 2.0 \times 10^5 \text{ lbs} \times 454 \text{ g/lb} \]

Calculating this gives:

\[ \text{Weight in grams} = 2.0 \times 10^5 \times 454 = 908 \times 10^5 \text{ g} \]

### Step 2: Calculate the number of moles of copper
The atomic weight of copper (Cu) is \(63.5 \text{ g/mol}\). To find the number of moles, we use the formula:

\[ \text{Number of moles} = \frac{\text{Weight in grams}}{\text{Molar mass}} \]

Substituting the values:

\[ \text{Number of moles} = \frac{908 \times 10^5 \text{ g}}{63.5 \text{ g/mol}} \]

Calculating this gives:

\[ \text{Number of moles} \approx 14.299 \times 10^5 \text{ moles} \]

### Step 3: Calculate the number of atoms
Using Avogadro's number, which is \(6.022 \times 10^{23} \text{ atoms/mol}\), we can find the total number of atoms:

\[ \text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number} \]

Substituting the values:

\[ \text{Number of atoms} = 14.299 \times 10^5 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} \]

Calculating this gives:

\[ \text{Number of atoms} \approx 86.109 \times 10^{28} \text{ atoms} \]

### Step 4: Express the answer in scientific notation
To express \(86.109 \times 10^{28}\) in proper scientific notation, we can write:

\[ \text{Number of atoms} \approx 8.61 \times 10^{29} \text{ atoms} \]

### Final Answer
The number of atoms of copper in the Statue of Liberty is approximately \(8.61 \times 10^{29}\) atoms.

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