Question

By using photons of specific wavelengths, chemists can dissociate gaseous HI to produce H atoms with certain speeds. When HI dissociates, the H atoms move away rapidly, whereas the heavier I atoms move more slowly.
(c) If this excess energy is carried away by the H atom as kinetic energy, what is its speed (in m/s)?

Answer 1

If a photon of 254 nm is used, the excess energy (in J) over that needed for dissociation is 2.93 10^-19 J. If this excess energy is carried away by the H atom as kinetic energy, then the speed is equal to the 2.4× 10^(-8) m/s..

What is Dissociation energy?

The bond-dissociation energy is defined as measure of the strength of a chemical bond which is represented as A−B. It can also be defined as the standard enthalpy change when the bond A−B is cleaved by homolysis to give two fragments A and B, that are usually radical species.

Energy of photon with λ 254 nm is given as

E = hC \ λ

= 6.626 × 10-³⁴ JS × 3 × 10 8 ms -1 /254 × 10 -9 m

= 7.83 10^-19 J

As we know that,

dissociation energy of HI = 295 10³ J. mol-¹

= 295 × 10³ J / mol -¹ / 6.023 × 10²³ mol -¹

= 4.898 × 10^-19 J.

Hence excess energy over dissociation

= 7.83 × 10^-19 J – 4.448 × 10^-19 J

= 2.93 × 10^-19 J

K.E = 2.93 × 10^-19 J

As we know that,

K.E = 1/2 of mv^2

mass of hydrogen atom = 1g = 10^(-3) kg.

2 × 2.93 × 10^-16 J = mv^2

v^2 = 5.86 × 10^(-16)

v = 2.42 × 10^(-8) m/s.

Thus, we concluded that the speed of H atom is

2.4× 10^(-8) m/s.

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