The dissociation energy of `H_(2)` is `430.53 kJ mol^(-1), `If `H_(2)` is of dissociated by illumination with radiation of wavelength `253.7 nm` , the fraction of the radiant energy which will be converted into ikinetic energy is given by

Explanation

To solve the problem, we need to follow these steps:

### Step 1: Convert Dissociation Energy to Joules per Molecule
The dissociation energy of \( H_2 \) is given as \( 430.53 \, \text{kJ/mol} \). We need to convert this energy into joules per molecule.

\[ \text{Dissociation Energy (in Joules)} = 430.53 \, \text{kJ/mol} \times 10^3 \, \text{J/kJ} = 430530 \, \text{J/mol} \]

To convert this to joules per molecule, we divide by Avogadro's number (\( N_A = 6.022 \times 10^{23} \, \text{molecules/mol} \)):

\[ E_{\text{dissociation}} = \frac{430530 \, \text{J/mol}}{6.022 \times 10^{23} \, \text{molecules/mol}} \approx 7.15 \times 10^{-19} \, \text{J/molecule} \]

### Step 2: Calculate Energy of a Photon
The energy of a photon can be calculated using the formula:

\[ E_{\text{photon}} = \frac{hc}{\lambda} \]

Where:
- \( h = 6.626 \times 10^{-34} \, \text{J s} \) (Planck's constant)
- \( c = 3.00 \times 10^8 \, \text{m/s} \) (speed of light)
- \( \lambda = 253.7 \, \text{nm} = 253.7 \times 10^{-9} \, \text{m} \)

Now substituting the values:

\[ E_{\text{photon}} = \frac{(6.626 \times 10^{-34} \, \text{J s})(3.00 \times 10^8 \, \text{m/s})}{253.7 \times 10^{-9} \, \text{m}} \approx 7.83 \times 10^{-19} \, \text{J/molecule} \]

### Step 3: Calculate Energy Converted to Kinetic Energy
The energy converted to kinetic energy when \( H_2 \) dissociates is the difference between the energy of the photon and the dissociation energy.

\[ E_{\text{kinetic}} = E_{\text{photon}} - E_{\text{dissociation}} = 7.83 \times 10^{-19} \, \text{J/molecule} - 7.15 \times 10^{-19} \, \text{J/molecule} = 0.68 \times 10^{-19} \, \text{J/molecule} \]

### Step 4: Calculate the Fraction of Energy Converted to Kinetic Energy
To find the fraction of the radiant energy that is converted into kinetic energy, we use the formula:

\[ \text{Fraction} = \frac{E_{\text{kinetic}}}{E_{\text{photon}}} \]

Substituting the values:

\[ \text{Fraction} = \frac{0.68 \times 10^{-19} \, \text{J/molecule}}{7.83 \times 10^{-19} \, \text{J/molecule}} \approx 0.0868 \]

### Step 5: Convert Fraction to Percentage
To express the fraction as a percentage:

\[ \text{Percentage} = \text{Fraction} \times 100 \approx 0.0868 \times 100 \approx 8.68\% \]

### Final Answer
The fraction of the radiant energy which will be converted into kinetic energy is approximately **8.68%**.

---