Highly reactive oxygen atoms in the ground electronic state, O(3P) (16 amu), can

Question

Highly reactive oxygen atoms in the ground electronic state, O(3P) (16 amu), can be generated from NO2 by laser induced dissociation: NO2 + hv rightarrow NO (v', J=0). The dissociation of an N-O bond in NO2 costs 201 kJ/mol for the formation of a v'=0 NO fragment and an O(3P) atom at rest The oxygen atoms generated in this way show two peaks in their velocity distribution: most oxygen atoms come either with a velocity of 900.00 m/s or with a velocity of 1872.92 m/s. The reaction is performed with laser light having a wavelength of 355 nm. Besides the oxygen atoms, NO (fundamental vibrational wavenumber 1804.4 cm-1) molecules arc generated in two vibrational states with different quantum numbers v', in the rotational groundstate (J'=0) in both cases. Calculate the two vibrational quantum numbers,v', of the produced NO molecules which correspond to the oxygen velocity peaks (round your v' values to next nearest integer numbers). If the NO fragments arc injected with a total of 12000 cm-1 of energy- that is used to accelerate the NO molecules and to excite them from v'=0 into the levels calculated above (J'=0), calculate the final speeds of the two excited NO species (mass of N: 14 amu; hint in case you made a mistake in a: the levels are v'=5 and v'=6).

Explanation / Answer

(a) E = 0.5xmxv2

E = 0.5x(0.016Kg/moL/6.022x1023 moL)x(900 m.s-1)2

E = 1.07x10-20 J (First peak)

E = 0.5xmxv2

E = 0.5x(0.016Kg/moL/6.022x1023 moL)x(1872.72 m.s-1)2

E = 4.66x10-20 J (Second peak)

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