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

Options

A. `4.946xx10^(2)`
B. `4.946xx10^(3)`
C. `4.946xx10^(4)`
D. `4.946xx10^(5)`

Answer

To calculate the ionization energy of sodium in kJ/mol given that electromagnetic radiation of wavelength 242 nm is sufficient to ionize the sodium atom, we can follow these steps:

### Step-by-Step Solution:

1. **Convert Wavelength to Meters**:
The wavelength given is in nanometers (nm). To convert it to meters (m), we use the conversion factor:
\[ 1 \text{ nm} = 10^{-9} \text{ m} \]
Therefore,
\[ \text{Wavelength} = 242 \text{ nm} = 242 \times 10^{-9} \text{ m} = 2.42 \times 10^{-7} \text{ m} \]

2. **Use the Energy Formula**:
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) = \(3.00 \times 10^{8} \text{ m/s}\)
- \(\lambda\) = wavelength in meters

3. **Substitute the Values**:
Plugging in the values:
\[ E = \frac{(6.626 \times 10^{-34} \text{ J s}) \times (3.00 \times 10^{8} \text{ m/s})}{2.42 \times 10^{-7} \text{ m}} \]

4. **Calculate the Energy**:
Performing the calculation:
\[ E = \frac{1.9878 \times 10^{-25} \text{ J m}}{2.42 \times 10^{-7} \text{ m}} \approx 8.22 \times 10^{-19} \text{ J} \]

5. **Convert Energy to kJ/mol**:
To convert the energy from joules to kilojoules per mole, we use Avogadro's number (\(N_A = 6.022 \times 10^{23} \text{ mol}^{-1}\)):
\[ \text{Energy in kJ/mol} = E \times N_A \times \frac{1 \text{ kJ}}{1000 \text{ J}} \]
\[ \text{Energy in kJ/mol} = (8.22 \times 10^{-19} \text{ J}) \times (6.022 \times 10^{23} \text{ mol}^{-1}) \times \frac{1 \text{ kJ}}{1000 \text{ J}} \]

6. **Final Calculation**:
\[ \text{Energy in kJ/mol} \approx 494.0 \text{ kJ/mol} \]

### Final Answer:
The ionization energy of sodium is approximately **494 kJ/mol**.

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