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

Explanation

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

### Step 1: Understand the Avogadro Number
The Avogadro number is defined as \(6.022 \times 10^{23}\). This is the number of particles (in this case, wheat grains) in one mole of a substance.

### Step 2: Identify the Distribution Rate
We are given that \(10^{10}\) grains are distributed each second. This means that every second, \(10^{10}\) grains are being handed out.

### Step 3: Calculate the Time Required
To find the time required to distribute \(6.022 \times 10^{23}\) grains at the rate of \(10^{10}\) grains per second, we can use the formula:

\[ \text{Time} = \frac{\text{Total number of grains}}{\text{Grains distributed per second}} \]

Substituting the values we have:

\[ \text{Time} = \frac{6.022 \times 10^{23}}{10^{10}} \]

### Step 4: Simplify the Calculation
Now, we simplify the expression:

\[ \text{Time} = 6.022 \times 10^{23 - 10} = 6.022 \times 10^{13} \text{ seconds} \]

### Final Answer
Thus, the time it would take to distribute one Avogadro number of wheat grains is:

\[ 6.022 \times 10^{13} \text{ seconds} \]

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