How much time (in hours) would it take to distribute one Avogadro number of wheat grains if `10^(20)` grains are distributed each second?

Options

A. 16.73
B. 1.673
C. 167.3
D. 1673

Answer

To solve the problem of how much time it would take to distribute one Avogadro number of wheat grains at a rate of \(10^{20}\) grains per second, we can follow these steps:

### Step 1: Identify Avogadro's Number
Avogadro's number is \(6.022 \times 10^{23}\) grains.

### Step 2: Determine the Rate of Distribution
The rate of distribution is given as \(10^{20}\) grains per second.

### Step 3: Calculate the Time in Seconds
To find the total time in seconds required to distribute \(6.022 \times 10^{23}\) grains, we can use the formula:

\[ \text{Time (in seconds)} = \frac{\text{Total grains}}{\text{Grains per second}} \]

Substituting the values:

\[ \text{Time (in seconds)} = \frac{6.022 \times 10^{23}}{10^{20}} = 6.022 \times 10^{3} \text{ seconds} \]

### Step 4: Convert Seconds to Hours
To convert seconds into hours, we use the conversion factor that there are 3600 seconds in an hour:

\[ \text{Time (in hours)} = \frac{\text{Time (in seconds)}}{3600} \]

Substituting the calculated time in seconds:

\[ \text{Time (in hours)} = \frac{6.022 \times 10^{3}}{3600} \approx 1.673 \text{ hours} \]

### Final Answer
It would take approximately **1.673 hours** to distribute one Avogadro number of wheat grains.

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