Calculate the Einstein when the frequency of photon is `10^(10)` kHz.

Explanation

To calculate the energy of one mole of photons (Einstein) when the frequency of a photon is given as \(10^{10}\) kHz, we can follow these steps:

### Step 1: Convert Frequency to Hertz
The frequency is given in kilohertz (kHz), so we need to convert it to hertz (Hz).
1 kHz = \(10^3\) Hz, thus:
\[ \nu = 10^{10} \text{ kHz} = 10^{10} \times 10^3 \text{ Hz} = 10^{13} \text{ Hz} \]

### Step 2: Use the Formula for Energy of One Photon
The energy \(E\) of one photon can be calculated using the formula:
\[ E = h \cdot \nu \]
where:
- \(h\) (Planck's constant) = \(6.626 \times 10^{-34} \text{ J s}\)
- \(\nu\) = frequency in Hz

Substituting the values:
\[ E = 6.626 \times 10^{-34} \text{ J s} \times 10^{13} \text{ Hz} \]

### Step 3: Calculate Energy of One Photon
Calculating the above expression:
\[ E = 6.626 \times 10^{-34} \times 10^{13} = 6.626 \times 10^{-21} \text{ J} \]

### Step 4: Calculate Energy of One Mole of Photons
To find the energy of one mole of photons (Einstein), we use Avogadro's number (\(N_A\)):
\[ E_{\text{mole}} = N_A \cdot E \]
where:
- \(N_A = 6.022 \times 10^{23} \text{ mol}^{-1}\)

Substituting the values:
\[ E_{\text{mole}} = 6.022 \times 10^{23} \text{ mol}^{-1} \times 6.626 \times 10^{-21} \text{ J} \]

### Step 5: Calculate Energy of One Mole of Photons
Calculating the above expression:
\[ E_{\text{mole}} = 6.022 \times 6.626 \times 10^{2} \text{ J} = 39.87 \times 10^{2} \text{ J} = 3.987 \times 10^{3} \text{ J} \]
To convert this to kilojoules:
\[ E_{\text{mole}} = 3.987 \text{ kJ/mol} \]

### Final Answer
The energy of one mole of photons (Einstein) is:
\[ \text{Einstein} = 3.987 \text{ kJ/mol} \]

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