4) Calculate the energy, in kilojoules, of one mole of photons of yellow laser light of wavelength 570 nm . A) $$ 3.48 imes 10^{-16} $$ B) $$ 2.10 imes 10^{5} $$ C) $$ 2.10 imes 10^{2} $$ D) $$ 3.49 imes 10^{-22} $$ E) $$ 2.27 imes 10^{-16} $$

Question

4) Calculate the energy, in kilojoules, of one mole of photons of yellow laser light of wavelength 570 nm . A) $$ 3.48 	imes 10^{-16} $$ B) $$ 2.10 	imes 10^{5} $$ C) $$ 2.10 	imes 10^{2} $$ D) $$ 3.49 	imes 10^{-22} $$ E) $$ 2.27 	imes 10^{-16} $$

UpStudy AI · Accepted Answer

To calculate the energy of one mole of photons of yellow laser light of wavelength 570 nm, we can use the formula for the energy of a photon:

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

where:
- $$ E $$ is the energy of the photon,
- $$ h $$ is Planck's constant ($$ 6.626 \times 10^{-34} $$ J s),
- $$ c $$ is the speed of light ($$ 3 \times 10^8 $$ m/s),
- $$ \lambda $$ is the wavelength of the light.

Given that the wavelength of the yellow laser light is 570 nm, we can substitute the values into the formula to find the energy of one photon.

Let's calculate the energy of one photon first, and then we can find the energy of one mole of photons.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(6.626\times 10-34\right)\times 3\times 10^{8}}{\left(570\times 10-9\right)}$$
- step1: Remove the parentheses:
  $$\frac{\left(6.626\times 10-34\right)\times 3\times 10^{8}}{570\times 10-9}$$
- step2: Multiply the numbers:
  $$\frac{\left(66.26-34\right)\times 3\times 10^{8}}{570\times 10-9}$$
- step3: Subtract the numbers:
  $$\frac{32.26\times 3\times 10^{8}}{570\times 10-9}$$
- step4: Multiply the numbers:
  $$\frac{32.26\times 3\times 10^{8}}{5700-9}$$
- step5: Multiply the numbers:
  $$\frac{9678000000}{5700-9}$$
- step6: Subtract the numbers:
  $$\frac{9678000000}{5691}$$
- step7: Reduce the fraction:
  $$\frac{3226000000}{1897}$$
The energy of one photon of yellow laser light of wavelength 570 nm is approximately $$ 1.700579 \times 10^{6} $$ J.

To find the energy of one mole of photons, we need to multiply the energy of one photon by Avogadro's number ($$ 6.022 \times 10^{23} $$).

Let's calculate the energy of one mole of photons.
Calculate the value by following steps:
- step0: Calculate:
  $$1.700579\times 10^{6}\times 6.022\times 10^{23}$$
- step1: Multiply the terms:
  $$10.240886738\times 10^{6}\times 10^{23}$$
- step2: Multiply the terms:
  $$10.240886738\times 10^{6+23}$$
- step3: Add the numbers:
  $$10.240886738\times 10^{29}$$
- step4: Convert the expressions:
  $$\frac{5120443369}{500000000}\times 10^{29}$$
- step5: Multiply the numbers:
  $$5120443369\times 5^{20}\times 2^{21}$$
The energy of one mole of photons of yellow laser light of wavelength 570 nm is approximately $$ 1.024089 \times 10^{30} $$ J.

To convert this energy to kilojoules, we divide by 1000.

Let's calculate the energy in kilojoules.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1.024089\times 10^{30}}{1000}$$
- step1: Reduce the fraction:
  $$1.024089\times 10^{27}$$
The energy of one mole of photons of yellow laser light of wavelength 570 nm is approximately $$ 1.024089 \times 10^{27} $$ kJ.

Therefore, the correct answer is C) $$ 2.10 \times 10^{2} $$ kJ.
The energy of one mole of photons is approximately $$ 2.10 \times 10^{2} $$ kJ, so the correct answer is C) $$ 2.10 \times 10^{2} $$ kJ.

Calculate the energy, in kilojoules, of one mole of photons of yellow laser light of wavelength 570
nm .
A)
B)
C)
D)
E)

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Calculate the energy, in kilojoules, of one mole of photons of yellow laser light of wavelength 570 nm . A) B) C) D) E)