QuestionJuly 22, 2025

Photons of a certain infrared light have an energy of 1.91times 10^-19J (a) What is the frequency of this IR light? square Hz (b) Use lambda =c/f to calculate its wavelength in nanometers. square nm

Photons of a certain infrared light have an energy of 1.91times 10^-19J (a) What is the frequency of this IR light? square Hz (b) Use lambda =c/f to calculate its wavelength in nanometers. square nm
Photons of a certain infrared light have an energy of 1.91times 10^-19J (a) What is the frequency of this IR light? square Hz (b) Use lambda =c/f to calculate its wavelength in nanometers. square nm

Solution
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Answer

(a) 2.88 \times 10^{14} \, \text{Hz} ### (b) 1040 \, \text{nm} Explanation 1. Calculate the frequency Use the formula for energy of a photon: E = hf, where h = 6.626 \times 10^{-34} \, \text{J}\cdot\text{s} is Planck's constant. Rearrange to find frequency: f = \frac{E}{h}. Substitute E = 1.91 \times 10^{-19} \, \text{J} to get f = \frac{1.91 \times 10^{-19}}{6.626 \times 10^{-34}}. 2. Calculate the wavelength Use the formula \lambda = \frac{c}{f}, where c = 3.00 \times 10^8 \, \text{m/s} is the speed of light. Convert the result to nanometers by multiplying by 10^9.

Explanation

1. Calculate the frequency<br /> Use the formula for energy of a photon: $E = hf$, where $h = 6.626 \times 10^{-34} \, \text{J}\cdot\text{s}$ is Planck's constant. Rearrange to find frequency: $f = \frac{E}{h}$. Substitute $E = 1.91 \times 10^{-19} \, \text{J}$ to get $f = \frac{1.91 \times 10^{-19}}{6.626 \times 10^{-34}}$.<br /><br />2. Calculate the wavelength<br /> Use the formula $\lambda = \frac{c}{f}$, where $c = 3.00 \times 10^8 \, \text{m/s}$ is the speed of light. Convert the result to nanometers by multiplying by $10^9$.
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