What is the wavelength in meters of 91.0 kJ/mol

Expert Solution

Ans- 1 mole *(6.02 x 10²³) of photons have 91.0 kJ/mol of energy,so the energy of a single photon. 91.0 kilojoules to joules by multiplying by 1,000. This equals 91000 joules. Next, divide this number by 6.02 x 10²³ photons to find the energy in a single photon:

(9.1 x 10⁴ J) / (6.02 x 10²³ photons) = 1.51 x 10^-19 J/photon

The formula for the energy of a photon is

energy = Planck's constant x frequency

Unfortunately, it does not contain the wavelength so we need enother equation:

speed of light = frequency x wavelength
frequency = speed of light / wavelength

Substituting for frequency in the top equation, we get:

energy = (Planck's constant x speed of light) / wavelength
wavelength x energy = Planck's constant x speed of light
wavelength = (Planck's constant x speed of light) / energy

The speed of light in a vacuum is a universal constant equal to 3 x 10⁸ m/s. Plack's constant is given as 6.63 × 10⁻³⁴ J∙s . Substituting in the above equation we get:

wavelength = [(6.63 × 10⁻³⁴ J∙s)(3x 10⁸ m/s)] / (1.51 x 10^-19 J) = 1.31 x 10^-6 m.

The wavelength of photons with the energy of 91.0 kJ/mol is 1.31 x 10^-6 meter.

queen_honey_blossom answered 11 months ago

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