Question

which statement regarding the relative energies of monochromatic light with with λ = 800 nm andmonochromatic light with λ = 400 nm is correct?(A) 800 nm light has half as much energy per mole of photons as 400 nm light.(B) 800 nm light has the same energy per mole of photons as 400 nm light.(C) 800 nm light has twice as much energy per mole of photons as 400 nm light.(D) No conclusion may be drawn regarding the relative energy per mole of photons without knowing the intensity of the light.

Answer 1

Answer:

The correct answer is option A.

Explanation:

Energy of the photon of an electromagnetic radiation is give by Planck's equation:

$E=\frac{hc}{\lambda }$

Where:

h = Planck's constant

c = speed of light

$\lambda$ = Wavelength of the photon's radiation

Energy of photon of 800 nm monochromatic light

$\lambda = 800 nm=400\times 10^{-9} m$

$E=\frac{hc}{800 \times 10^{-9} m}$

Energy per mole of photons:

$E\times N_A=\frac{hc}{800 \times 10^{-9} m}\times 6.022\times 10^{23} mol^{-1}$..[1]

Energy of photon of 400 nm monochromatic light

$\lambda '= 400 nm=400\times 10^{-9} m$

Energy per mole of photons:

$E'\times N_A=\frac{hc}{400 \times 10^{-9} m}\times 6.022\times 10^{23} mol^{-1}$..[2]

[1] ÷ [2]

$\frac{E\times N_A}{E'\times N_A}=\frac{\frac{hc\trimes 6.022\times 10^{23} mol^{-1}}{800 \times 10^{-9} m}}{\frac{hc\times 6.022\times 10^{23} mol^{-1}}{400 \times 10^{-9} m}}$

$\frac{E}{E'}=\frac{1}{2}$

$E=\frac{1}{2}\times E'$

Answer 2

Answer:

800 nm light has half as much energy per mole of photons as 400 nm light. (Option A is correct)

Explanation:

Step 1: Data given

photon 1 has a wavelength of 800 nm

photon 2 has a wavelength of 400 nm

Speed of light = 3*10^8 m/s

Planck's constant = 6.6 * 10^-34 J*s

Step 2: Calculate energy at 800 nm

E = (h*c)/ λ

⇒ with E = the particular photon energy

⇒ with h = The Planck constant = 6.6 * 10^-34 J*s

⇒ with c = the speed of light = 3*10^8 m/s

⇒ with  λ = the wavelength of the light = 800 nm = 8*10^-7 m

E = (6.6 * 10^-34 * 3*10^8) / 8*10^-7

E = 2.5 * 10^-19 J

Step 3: Calculate energy at 400 nm

E = (h*c)/ λ

⇒ with E = the particular photon energy

⇒ with h = The Planck constant = 6.6 * 10^-34 J*s

⇒ with c = the speed of light = 3*10^8 m/s

⇒ with  λ = the wavelength of the light = 400 nm = 4*10^-7 m

E = (6.6 * 10^-34 * 3*10^8) / 4*10^-7

E = 4.95 * 10^-19 J

Since in 1 mol of photons we have the same amount of photons at 400 nm and 800 nm, this won'tchange the ratio.

E(800nm) /E(400nm) = 2.5 * 10^-19 J / 4.95 * 10^-19 J

E(800nm) /E(400nm) = 1/2

This means 800 nm light has half as much energy per mole of photons as 400 nm light. (Option A is correct)