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 using the given wavelength of electromagnetic radiation (242 nm), we can follow these steps:

### Step 1: Convert Wavelength to Meters
The wavelength is given in nanometers (nm). We need to convert it to meters (m) for our calculations.

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

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

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

Where:
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J s} \))
- \( c \) is the speed of light (\( 3.00 \times 10^{8} \, \text{m/s} \))
- \( \lambda \) is the wavelength in meters

### Step 3: Substitute Values into the Formula
Substituting the values into the formula:

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

### Step 4: Calculate the Energy
Now, calculate the energy:

\[ E = \frac{(6.626 \times 10^{-34}) \times (3.00 \times 10^{8})}{242 \times 10^{-9}} \]
\[ E \approx \frac{1.9878 \times 10^{-25}}{242 \times 10^{-9}} \approx 8.22 \times 10^{-19} \, \text{J} \]

### Step 5: Convert Energy to kJ/mol
To find the ionization energy in kJ/mol, we need to convert joules to kilojoules and multiply by Avogadro's number (\( 6.022 \times 10^{23} \, \text{atoms/mol} \)):

\[ E_{\text{per mole}} = E \times N_A = (8.22 \times 10^{-19} \, \text{J}) \times (6.022 \times 10^{23} \, \text{atoms/mol}) \]
\[ E_{\text{per mole}} \approx 4.95 \times 10^{5} \, \text{J/mol} \]

Convert to kJ/mol:

\[ E_{\text{per mole}} \approx 495 \, \text{kJ/mol} \]

### Final Answer
The ionization energy of sodium is approximately **495 kJ/mol**.

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