Calculate the energy of one mole of photons of radiation whose frequency is `5 xx 10^(14) Hz`.

Options

A. 199.51 kJ
B. `3.3xx10^(-19)J`
C. `6.626xx10^(-34)J`
D. `2.31xx10^(5)J`

Explanation

To calculate the energy of one mole of photons of radiation whose frequency is \(5 \times 10^{14} \, \text{Hz}\), we can follow these steps:

### Step 1: Calculate the energy of one photon
The energy \(E\) of a single photon can be calculated using the formula:
\[ E = h \nu \]
where:
- \(E\) = energy of one photon (in joules)
- \(h\) = Planck's constant = \(6.626 \times 10^{-34} \, \text{J s}\)
- \(\nu\) = frequency of the radiation = \(5 \times 10^{14} \, \text{Hz}\)

Substituting the values:
\[ E = (6.626 \times 10^{-34} \, \text{J s}) \times (5 \times 10^{14} \, \text{Hz}) \]

### Step 2: Perform the multiplication
Calculating the above expression:
\[ E = 6.626 \times 5 \times 10^{-34} \times 10^{14} = 33.13 \times 10^{-20} \, \text{J} \]
Simplifying this:
\[ E = 3.313 \times 10^{-19} \, \text{J} \]

### Step 3: Calculate the energy for one mole of photons
To find the energy for one mole of photons, we use Avogadro's number (\(N_A\)):
\[ N_A = 6.022 \times 10^{23} \, \text{photons/mol} \]
The energy for one mole of photons is given by:
\[ E_{\text{mole}} = N_A \times E \]
Substituting the values:
\[ E_{\text{mole}} = (6.022 \times 10^{23}) \times (3.313 \times 10^{-19} \, \text{J}) \]

### Step 4: Perform the multiplication
Calculating the above expression:
\[ E_{\text{mole}} = 6.022 \times 3.313 \times 10^{23} \times 10^{-19} = 19.91 \times 10^{4} \, \text{J} \]
Simplifying this:
\[ E_{\text{mole}} = 199.1 \, \text{kJ} \]

### Final Answer
Thus, the energy of one mole of photons is approximately:
\[ \boxed{199.1 \, \text{kJ}} \]