When the universal gas constant (R) is divided by Avogadro's number `(N_(0))`, their ration is called

Options

A. Planck's constant
B. Rydberg constant
C. Boltzmann constant
D. van der Waal's constant

Explanation

To solve the question, we need to understand the relationship between the universal gas constant (R) and Avogadro's number (N₀). Here’s a step-by-step breakdown:

### Step 1: Understand the Definitions
- **Universal Gas Constant (R)**: This is a constant used in the ideal gas law, typically expressed as \( R = 8.31 \, \text{J K}^{-1} \text{mol}^{-1} \).
- **Avogadro's Number (N₀)**: This is the number of particles (atoms, molecules, etc.) in one mole of a substance, approximately \( N₀ = 6.022 \times 10^{23} \, \text{mol}^{-1} \).

### Step 2: Set Up the Equation
We need to find the ratio of the universal gas constant (R) to Avogadro's number (N₀):
\[ \text{Ratio} = \frac{R}{N₀} \]

### Step 3: Substitute the Values
Substituting the known values into the equation:
\[ \text{Ratio} = \frac{8.31 \, \text{J K}^{-1} \text{mol}^{-1}}{6.022 \times 10^{23} \, \text{mol}^{-1}} \]

### Step 4: Simplify the Units
When we divide these two quantities, the units of "mol" in the numerator and denominator cancel out:
\[ \text{Ratio} = \frac{8.31 \, \text{J K}^{-1}}{6.022 \times 10^{23}} = \text{J K}^{-1} \]

### Step 5: Calculate the Value
Now, performing the calculation:
\[ \text{Ratio} \approx 1.38 \times 10^{-23} \, \text{J K}^{-1} \]

### Conclusion
The ratio of the universal gas constant (R) to Avogadro's number (N₀) is known as the **Boltzmann constant (k)**, which is approximately \( k \approx 1.38 \times 10^{-23} \, \text{J K}^{-1} \).

### Final Answer
The ratio of the universal gas constant (R) divided by Avogadro's number (N₀) is called the **Boltzmann constant**.

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