The bond energy of H2 molecule is 104 Kcal per mole. If an electromagnetic radiation of 200 nm falls on a H2 molecule, then what is the maximum kinetic energy of each hydrogen atom?

To determine the maximum kinetic energy of each hydrogen atom when electromagnetic radiation of 200 nm interacts with an H2 molecule, we first need to understand the relationship between energy, wavelength, and the bond energy of the molecule.

Understanding Bond Energy

The bond energy of a molecule, in this case, H2, is the amount of energy required to break the bond between the two hydrogen atoms. For H2, this value is given as 104 kcal per mole. To work with this in our calculations, we should convert it into joules, as energy from electromagnetic radiation is typically expressed in joules.

Conversion of Bond Energy

1 kcal is approximately equal to 4184 joules. Therefore, we can convert the bond energy of H2:

• 104 kcal/mol × 4184 J/kcal = 435,776 J/mol

Since this value is per mole, we need to convert it to the energy per molecule. Using Avogadro's number (approximately 6.022 × 10²³ molecules/mol), we find:

• Energy per molecule = 435,776 J/mol ÷ 6.022 × 10²³ molecules/mol ≈ 7.24 × 10⁻¹⁹ J

Calculating Energy of the Electromagnetic Radiation

Next, we need to calculate the energy of the electromagnetic radiation with a wavelength of 200 nm. The energy of a photon can be calculated using the formula:

E = hc/λ

Where:

• E is the energy of the photon
• h is Planck's constant (6.626 × 10⁻³⁴ J·s)
• c is the speed of light (3.00 × 10⁸ m/s)
• λ is the wavelength in meters (200 nm = 200 × 10⁻⁹ m)

Plugging in the values:

• E = (6.626 × 10⁻³⁴ J·s)(3.00 × 10⁸ m/s) / (200 × 10⁻⁹ m)
• E ≈ 9.93 × 10⁻¹⁴ J

Finding Maximum Kinetic Energy

Now, we can find the maximum kinetic energy of each hydrogen atom. The maximum kinetic energy (KE) of the hydrogen atoms after absorbing the photon can be calculated using the formula:

KE = E_photon - Bond Energy

Substituting the values we calculated:

• KE = 9.93 × 10⁻¹⁴ J - 7.24 × 10⁻¹⁹ J

Since the bond energy is significantly smaller than the energy of the photon, we can approximate:

• KE ≈ 9.93 × 10⁻¹⁴ J

Final Conversion to Kcal

If you want to express this kinetic energy in kcal, we can convert it back:

• KE in kcal = 9.93 × 10⁻¹⁴ J ÷ 4184 J/kcal ≈ 2.37 × 10⁻¹⁷ kcal

In summary, the maximum kinetic energy of each hydrogen atom after the interaction with the 200 nm electromagnetic radiation is approximately 9.93 × 10⁻¹⁴ joules, or about 2.37 × 10⁻¹⁷ kcal. This illustrates how energy from electromagnetic radiation can significantly exceed the bond energy, resulting in the dissociation of the molecule and the kinetic energy of the atoms involved.