Respuesta :
Answer:
The correct answer is option A.
Explanation:
Energy of the photon of an electromagnetic radiation is give by Planck's equation:
[tex]E=\frac{hc}{\lambda }[/tex]
Where:
h = Planck's constant
c = speed of light
[tex]\lambda [/tex] = Wavelength of the photon's radiation
Energy of photon of 800 nm monochromatic light
[tex]\lambda = 800 nm=400\times 10^{-9} m[/tex]
[tex]E=\frac{hc}{800 \times 10^{-9} m}[/tex]
Energy per mole of photons:
[tex] E\times N_A=\frac{hc}{800 \times 10^{-9} m}\times 6.022\times 10^{23} mol^{-1}[/tex]..[1]
Energy of photon of 400 nm monochromatic light
[tex]\lambda '= 400 nm=400\times 10^{-9} m[/tex]
Energy per mole of photons:
[tex] E'\times N_A=\frac{hc}{400 \times 10^{-9} m}\times 6.022\times 10^{23} mol^{-1}[/tex]..[2]
[1] ÷ [2]
[tex]\frac{E\times N_A}{E'\times N_A}=\frac{\frac{hc\trimes 6.022\times 10^{23} mol^{-1}}{800 \times 10^{-9} m}}{\frac{hc\times 6.022\times 10^{23} mol^{-1}}{400 \times 10^{-9} m}}[/tex]
[tex]\frac{E}{E'}=\frac{1}{2}[/tex]
[tex]E=\frac{1}{2}\times E'[/tex]
The monochromatic light with 800 nm has half as much energy per mole of photons as the monochromatic light with 400 nm (option A).
The energy of one photon is given by:
[tex] E = h\frac{c}{\lambda} [/tex]
Where:
c: is the speed of light = 3.00x10⁸ m/s
h: is the Planck's constant = 6.62x10⁻³⁴ J*s
λ: is the wavelength of the light
We can find the energy per mole of photons with Avogadro's number:
[tex] E = h\frac{c}{\lambda}*6.022\cdot 10^{23} \:photons/mol [/tex]
For the monochromatic light with 800 nm, we have:
[tex] E_{800} = 6.62 \cdot 10^{-34} J*s\frac{3.00 \cdot 10^{8} m/s}{800 \cdot 10^{-9} m}*6.022\cdot 10^{23} \:photons/mol [/tex] (1)
And for the monochromatic light with 400 nm:
[tex] E_{400} = 6.62 \cdot 10^{-34} J*s\frac{3.00 \cdot 10^{8} m/s}{400 \cdot 10^{-9} m}*6.022\cdot 10^{23} \:photons/mol [/tex] (2)
Diving eq (2) by (1), we get:
[tex] \frac{E_{400}}{E_{800}} = \frac{6.62 \cdot 10^{-34} J*s\frac{3.00 \cdot 10^{8} m/s}{400 \cdot 10^{-9} m}*6.022\cdot 10^{23} \:photons/mol}{6.62 \cdot 10^{-34} J*s\frac{3.00 \cdot 10^{8} m/s}{800 \cdot 10^{-9} m}*6.022\cdot 10^{23} \:photons/mol} = 2 [/tex]
so
[tex] E_{800} = \frac{E_{400}}{2} [/tex]
Therefore, the 800 nm light has half as much energy per mole of photons as 400 nm light (option A).
Find more here:
- https://brainly.com/question/6576580?referrer=searchResults
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I hope it helps you!
