Calculate the value of Boltzmann constant `k_(B)`, Given `R = 8.3 xx 10^(3) J//kg-mol-K` and Avogadro number, ` N = 6.03 xx 10^(26)//kg-mol`.

Answer

To calculate the value of the Boltzmann constant \( k_B \), we can use the relationship between the universal gas constant \( R \) and Avogadro's number \( N_A \). The formula is given by:

\[ k_B = \frac{R}{N_A} \]

### Step 1: Identify the values of \( R \) and \( N_A \)
- Given \( R = 8.3 \times 10^3 \, \text{J/(kg-mol-K)} \)
- Given \( N_A = 6.03 \times 10^{26} \, \text{kg-mol} \)

### Step 2: Substitute the values into the formula
Now, we substitute the values of \( R \) and \( N_A \) into the formula for \( k_B \):

\[ k_B = \frac{8.3 \times 10^3 \, \text{J/(kg-mol-K)}}{6.03 \times 10^{26} \, \text{kg-mol}} \]

### Step 3: Perform the division
Now, we perform the division:

\[ k_B = \frac{8.3 \times 10^3}{6.03 \times 10^{26}} \, \text{J/K} \]

Calculating the numerical value:

\[ k_B = \frac{8.3}{6.03} \times 10^{3 - 26} \, \text{J/K} \]

\[ k_B \approx 1.376 \times 10^{-23} \, \text{J/K} \]

### Final Answer
Thus, the value of the Boltzmann constant \( k_B \) is approximately:

\[ k_B \approx 1.376 \times 10^{-23} \, \text{J/K} \]

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