By using photons of specific wavelengths, chemists can dissociate gaseous HI to
ID: 1056653 • Letter: B
Question
By using photons of specific wavelengths, chemists can dissociate gaseous HI to produce H atoms with accurately known speeds. When HI dissociates, the H atoms move away rapidly, whereas the relatively heavy I atoms move little. Use Table 9.2 in your textbook to answer the following questions: (a) What is the longest wavelength (in nm) that can dissociate a molecule of HI? 406 nm (b) If a photon of 238 nm is used, what is the excess energy (in J) over that needed for the dissociation? 208000 (c) If all of this excess energy is carried away by the H atom as kinetic energy, what is its speed (in m/s)? m/sExplanation / Answer
Energy having the ability of dissociation of a molecule of HI:
E = (6.636 x 10^-34 J.s)(3.00 x 10^8 m/s)/(4.06 x 10^-7 m)
solving it gives
= 4.90 x 10^-19 J
Energy of a photon with = 238 nm
= 238 nm(1 m)/(1 x 10^9 nm) = 2.38 x 10^-7 m
E = (6.636 x 10^-34 J.s)(3.00 x 10^8 m/s)/(2.38 x 10^-7 m) = 8.36 x 10^-19 J
Excess energy = 8,36 x 10^-19 J - 4.90 x 10^-19 J = 3.46 x 10^-19 J
So 3.46 x 10^-19 J is the excess energy that will contribute to the speed of the H atom.
Kinetic energy = Ek = (1/2)mv^2 = mv^2/2
v = sq root(2E/m) = sq root[2(3.46 x 10^-19 J)/(1.673 × 10^-27 kg)] = 1.43 x 10^4 m/s
Moving right along at 14381.0 m/s
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