Chapter 21: Problem 1

Visible light having a wavelength of $5 \times 10^{-7} \mathrm{m}$ appears green. Compute the frequency and energy of a photon of this light.

Short Answer

Expert verified

Question: Calculate the frequency and energy of a visible light photon with a wavelength of $5 \times 10^{-7} \mathrm{m}$. Answer: The frequency of the visible light photon is $6.00 \times 10^{14} \mathrm{Hz}$, and its energy is approximately $3.98 \times 10^{-19} \mathrm{J}$.

Step by step solution

Calculate the frequency

To calculate the frequency, we need to use the speed of light equation, which is: $$ c = \lambda \nu $$ Where: - $c$ is the speed of light ($3.00 \times 10^8 \mathrm{m/s}$) - $\lambda$ is the wavelength of light ($5 \times 10^{-7} \mathrm{m}$) We can rearrange the equation to solve for the frequency ($\nu$): $$ \nu = \frac{c}{\lambda} $$ Now, let's plug in the values and calculate the frequency of the photon: $$ \nu = \frac{3.00 \times 10^8 \mathrm{m/s}}{5 \times 10^{-7} \mathrm{m}} = 6.00 \times 10^{14} \mathrm{Hz} $$ The frequency of the green light photon is $6.00 \times 10^{14} \mathrm{Hz}$.

Calculate the energy

Now that we have the frequency, we can compute the energy of the photon using Planck's equation: $$ E = h\nu $$ Where: - $E$ is the energy of the photon - $h$ is the Planck's constant ($6.63 \times 10^{-34} \mathrm{Js}$) - $\nu$ is the frequency of the photon ($6.00 \times 10^{14} \mathrm{Hz}$) Plugging in the values and calculating the energy of the photon: $$ E = (6.63 \times 10^{-34} \mathrm{Js})(6.00 \times 10^{14} \mathrm{Hz}) = 3.978 \times 10^{-19} \mathrm{J} $$ The energy of the green light photon is approximately $3.98 \times 10^{-19} \mathrm{J}$.

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Visible light having a wavelength of \(5 \times 10^{-7} \mathrm{m}\) appears green. Compute the frequency and energy of a photon of this light.

Short Answer

Step by step solution

Calculate the frequency

Calculate the energy

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