The minimum energy needed to dissociate iodine molecules, I2, is 151 kJ/mol. What is the wavelength of photons (in nm) that supplies this energy, assuming each bond dissociated by absorbing one photon?
1 Answer
Explanation:
Equations this solution applied:
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N=n*N_AN=n⋅NA whereNN is the quantity ofnn moles of particles andN_A=6.02*10^23*"mol"^(-1)NA=6.02⋅1023⋅mol−1 is the Avagordoro's number -
The Planck's Law
E=h*fE=h⋅f whereEE is the energy of a single photon of frequencyff andhh is the Planck's Constant,h=6.63 × 10^(-34)* "m"^2* "kg" *"s"^(-1)= 6.63*10^(-34) color(blue)("J")*"s"h=6.63×10−34⋅m2⋅kg⋅s−1=6.63⋅10−34J⋅s [1] -
lambda=v/fλ=vf wherelambdaλ is the wavelength of a wave or an electromagnetic (EM) radiation of frequencyff .
From the question, breaking
where
Thus it takes
to break a single iodine molecule.
Apply the Planck's Law to find the maximum frequency of the EM radiation capable of breaking one such molecule:
*Make sure that you get the unit that corresponds to the quantity after canceling out corresponding pairs. Here we are expecting
Assuming
Sources:
1. Units ("dimensions") of the Planck's Constant: https://www.askiitians.com/forums/General-Physics/find-the-dimension-of-planck-constant-h-from-the-e_74309.htm