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# An unknown element was tested using a spectroscopic technique. Light was emitted from the sample at a wavelength of 525.6 nm. Calculate the energy of a photon and the energy of one mole of photons of the light.

We know that the energy of photon os given by the following equation-

E = hc/λ

Where  E = energy

h = Planck's constant= 6.6  × 10^-34 m²kg/s

c = speed of light = 3× 10^8 m/s

λ= wavelength

Energy of one photon = (6.626 x 10^-34 m^2 kg/s x 3 x 10^8 m/s) / 525.6 x 10^-9 m = 3.78 x 10^-19 J

1 mol photons = 6.023 x 10^23 photons

Energy of 1 mol of photons = (6.023 x 10^23 x 6.626 x 10^-34 m^2 kg/s x 3 x 10^8 m/s) / 525.6 x 10^-9 m

= 2.28 x 10^5 J

Step-by-step explanation:

Equation for the energy of a photon E = energy

h = Planck's constant

c = speed of light = wavelength

Energy of one photon = (6.626 x 10^-34 m^2 kg/s x 3 x 10^8 m/s) / 525.6 x 10^-9 m

3.78 x 10^-19 J

1 mol photons = 6.023 x 10^23 photons

Energy of 1 mol of photons = (6.023 x 10^23 x 6.626 x 10^-34 m^2 kg/s x 3 x 10^8 m/s) / 525.6 x 10^-9 m

2.28 x 10^5 J

Given,

λ(wavelength) = 525.6 nm = 525.6 x 10^-9 m

Part 1 :- calculation of energy of a photon of the light.

We know that,

E = hc/λ -------------> (i)

Here,

E = energy

h = Planck's constant = 6.626 x 10^-34 m^2 kg/s

c = speed of light = 3 x 10^8 m/s

Substituting the above values in equation (i) we have,

E = (6.626 x 10^-34 m^2 kg/s x 3 x 10^8 m/s) / 525.6 x 10^-9 m

=  3.78 x 10^-19 J

Part 2 :- calculation of energy of one mole of photons of the light.

In order to find the energy of one mole of photons of the light we have to multiply the calculated energy from part-1 with avogadro's number (NA).

Therefore, energy of one mole of photons of light =  3.78 x 10^-19 J X NA

= 3.78 x 10^-19 J X 6.022 x 10^23

= 2.28 x 10^5 J

Energy of one photon = 3.78 x 10^-19 J

Energy of 1 mol of photons = 2.28 x 10^5 J

Step-by-step explanation:
Equation for the energy of a photon E = energy

h = Planck's constant

c = speed of light = wavelength

Energy of one photon = (6.626 x 10^-34 m^2 kg/s x 3 x 10^8 m/s) / 525.6 x 10^-9 m

= 3.78 x 10^-19 J

1 mol photons = 6.023 x 10^23 photons

Energy of 1 mol of photons = (6.023 x 10^23 x 6.626 x 10^-34 m^2 kg/s x 3 x 10^8 m/s) / 525.6 x 10^-9 m

= 2.28 x 10^5 J Energy of a photon= Energy of a mole of photon= Step-by-step explanation:
See the attachment Energy of photon Energy of one mole of photon of light Step-by-step explanation:
Given:
h (Planck's constant) = c (speed of light) =  (wavelength of light) = 525.6 nm = Calculating for photon energy:    Calculating for energy of one mol of photon of light:

We need to multiply the energy of photon by Avogadro's constant    Energy of one photon = J

Energy of one mole photon = 227.749 kJ

Step-by-step explanation:

λ = 525.6nm

c = 3×108m/s

h = 6.626×10−34Js

Energy of one photon is:

E = hc / λ

E = 6.626×10−34 ×3×108 / 525.6×10−9

Energy of one mole photons = =227.749 kJ

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