QuestionJune 4, 2025

13. A photon has energy 3.98times 10^-19J What is its wavelength.?

13. A photon has energy 3.98times 10^-19J What is its wavelength.?
13. A photon has energy 3.98times 10^-19J What is its wavelength.?

Solution
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Answer

\lambda \approx 5.00 \times 10^{-7} \, \text{m} (or 500 nm) Explanation 1. Use the Energy-Wavelength Relationship The energy of a photon is related to its wavelength by the formula: **E = \frac{hc}{\lambda}**, where E is energy, h is Planck's constant (6.626 \times 10^{-34} \, \text{J}\cdot\text{s}), c is the speed of light (3.00 \times 10^8 \, \text{m/s}), and \lambda is the wavelength. 2. Solve for Wavelength Rearrange the formula to solve for \lambda: **\lambda = \frac{hc}{E}**. 3. Substitute Values Substitute h = 6.626 \times 10^{-34} \, \text{J}\cdot\text{s}, c = 3.00 \times 10^8 \, \text{m/s}, and E = 3.98 \times 10^{-19} \, \text{J} into the equation: \lambda = \frac{(6.626 \times 10^{-34})(3.00 \times 10^8)}{3.98 \times 10^{-19}}.

Explanation

1. Use the Energy-Wavelength Relationship<br /> The energy of a photon is related to its wavelength by the formula: **$E = \frac{hc}{\lambda}$**, where $E$ is energy, $h$ is Planck's constant ($6.626 \times 10^{-34} \, \text{J}\cdot\text{s}$), $c$ is the speed of light ($3.00 \times 10^8 \, \text{m/s}$), and $\lambda$ is the wavelength.<br />2. Solve for Wavelength<br /> Rearrange the formula to solve for $\lambda$: **$\lambda = \frac{hc}{E}$**.<br />3. Substitute Values<br /> Substitute $h = 6.626 \times 10^{-34} \, \text{J}\cdot\text{s}$, $c = 3.00 \times 10^8 \, \text{m/s}$, and $E = 3.98 \times 10^{-19} \, \text{J}$ into the equation: <br /> $\lambda = \frac{(6.626 \times 10^{-34})(3.00 \times 10^8)}{3.98 \times 10^{-19}}$.
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