Questions: What is the energy of a photon of yellow light whose wavelength is 489 nm? (Planck's constant, h = 6.626 x 10^-34 J . s; Speed of light = 3.0 x 10^8 m / s) 3.38 x 10^-28 J 4.07 x 10^-19 J 5.09 x 10^5 J 3.37 x 10^-19 J 3.37 x 10^-10 J

What is the energy of a photon of yellow light whose wavelength is 489 nm? (Planck's constant, h = 6.626 x 10^-34 J . s; Speed of light = 3.0 x 10^8 m / s) 3.38 x 10^-28 J 4.07 x 10^-19 J 5.09 x 10^5 J 3.37 x 10^-19 J 3.37 x 10^-10 J
Transcript text: What is the energy of a photon of yellow light whose wavelength is 489 nm ? (Planck's constant, $\boldsymbol{h}$ $=6.626 \times 10^{-34} \mathrm{~J} . \mathrm{s}$; Speed of light $=3.0 \times 10^{8} \mathrm{~m} / \mathrm{s}$ ) $3.38 \times 10^{-28} \mathrm{~J}$ $4.07 \times 10^{-19} \mathrm{~J}$ $5.09 \times 10^{5} \mathrm{~J}$ $3.37 \times 10^{-19} \mathrm{~J}$ $3.37 \times 10^{-10} \mathrm{~J}$
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Solution

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Solution Steps

Step 1: Understand the Problem

We need to calculate the energy of a photon of yellow light with a given wavelength of 489 nm. We will use the formula for the energy of a photon, which is given by:

\[ E = \frac{hc}{\lambda} \]

where:

  • \( E \) is the energy of the photon,
  • \( h = 6.626 \times 10^{-34} \, \text{J} \cdot \text{s} \) is Planck's constant,
  • \( c = 3.0 \times 10^{8} \, \text{m/s} \) is the speed of light,
  • \( \lambda = 489 \, \text{nm} = 489 \times 10^{-9} \, \text{m} \) is the wavelength of the light.
Step 2: Substitute Values into the Formula

Substitute the given values into the formula:

\[ E = \frac{(6.626 \times 10^{-34} \, \text{J} \cdot \text{s})(3.0 \times 10^{8} \, \text{m/s})}{489 \times 10^{-9} \, \text{m}} \]

Step 3: Perform the Calculation

Calculate the energy:

\[ E = \frac{(6.626 \times 10^{-34})(3.0 \times 10^{8})}{489 \times 10^{-9}} \]

\[ E = \frac{1.9878 \times 10^{-25}}{489 \times 10^{-9}} \]

\[ E = 4.0654 \times 10^{-19} \, \text{J} \]

Step 4: Match with Given Options

Compare the calculated energy with the given options. The closest match is:

\( 4.07 \times 10^{-19} \, \text{J} \)

Final Answer

\[ \boxed{4.07 \times 10^{-19} \, \text{J}} \]

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