Electromagnetic radiation of wavelength 242 nm is just sufficient to ionise the sodium atom . Calculate the ionisation energy of sodium in kJ `mol^(-1)`.

Options

A. `494.65`
B. `400`
C. `247`
D. `600`

Explanation

To calculate the ionization energy of sodium in kJ/mol given the wavelength of electromagnetic radiation, we can follow these steps:

### Step 1: Convert the wavelength from nanometers to meters
The wavelength is given as 242 nm. To convert this to meters, we use the conversion factor \(1 \text{ nm} = 10^{-9} \text{ m}\).

\[ \text{Wavelength} (\lambda) = 242 \text{ nm} = 242 \times 10^{-9} \text{ m} \]

### Step 2: Use the formula for energy of a photon
The energy (E) of a photon can be calculated using the formula:

\[ E = \frac{hc}{\lambda} \]

Where:
- \(h\) (Planck's constant) = \(6.626 \times 10^{-34} \text{ J s}\)
- \(c\) (speed of light) = \(3.00 \times 10^{8} \text{ m/s}\)
- \(\lambda\) = \(242 \times 10^{-9} \text{ m}\)

### Step 3: Substitute the values into the formula
Now we can substitute the values into the formula to find the energy:

\[ E = \frac{(6.626 \times 10^{-34} \text{ J s})(3.00 \times 10^{8} \text{ m/s})}{242 \times 10^{-9} \text{ m}} \]

### Step 4: Calculate the energy
Perform the calculation:

\[ E = \frac{(6.626 \times 10^{-34})(3.00 \times 10^{8})}{242 \times 10^{-9}} \approx 8.21 \times 10^{-19} \text{ J} \]

### Step 5: Convert the energy from joules to kJ/mol
To find the ionization energy per mole, we need to multiply the energy of one photon by Avogadro's number (\(N_A = 6.022 \times 10^{23} \text{ mol}^{-1}\)):

\[ \text{Ionization Energy} = E \times N_A = (8.21 \times 10^{-19} \text{ J}) \times (6.022 \times 10^{23} \text{ mol}^{-1}) \]

### Step 6: Calculate the ionization energy in joules
Perform the multiplication:

\[ \text{Ionization Energy} \approx 494.65 \text{ kJ/mol} \]

### Step 7: Final answer
Thus, the ionization energy of sodium is approximately:

\[ \text{Ionization Energy} \approx 494.65 \text{ kJ/mol} \]

### Summary
The ionization energy of sodium is approximately **494.65 kJ/mol**.

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