Calculating IR Energy: 1.614 x 107 MHz

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Homework Statement



What is the energy (in kJ/mol) of infrared radiation that has a frequency of 1.614 x 107 MHz?

Homework Equations



E = nhv

The Attempt at a Solution



3 x 6.63 x 10^-34 (J x s) multiplied by 1.614 x 10^7 (MHz) multiplied by (10^6 Hz/1 MHz) multiplied by (1 kJ/ 1000J) = 3.210246 x 10^-20, which is wrong.
 
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E = hv
v=1.614x10^13 hz
h = 6.63x10^-34
E = 1.07x10^-20 J
E/1000 = kJ
E = 1.07x10^-23 kJ
per mole
1.07x10^-23 * (6.02 x 10^23 atoms/mol)
E = 6.44 kJ/mol

hope that is clear, any questions let me know :)
 


nickdk said:
E = hv
v=1.614x10^13 hz
h = 6.63x10^-34
E = 1.07x10^-20 J
E/1000 = kJ
E = 1.07x10^-23 kJ
per mole
1.07x10^-23 * (6.02 x 10^23 atoms/mol)
E = 6.44 kJ/mol

hope that is clear, any questions let me know :)

Yes that's the right answer! But I'm still having trouble understanding why, in terms of units, you can multiply the last step by (6.02 x 10^23 atoms/mol) and still get units of (kJ/mol). When did the unit of "atoms" appear?

Reflection: I made the mistake of not properly converting the Si-Units of "Mega-x" to "x" and neglected the aspect of moles.