Questions: If a photon has energy of 3.74 × 10^-26 J, what is the wavelength of this photons in meters? h=6.626 × 10^-34 Js

Transcript text: 21 Formula 3 points If a photon has energy of $3.74 \times 10^{-26} \mathrm{~J}$, what is the wavelength of this photons in meters? \[ \mathrm{h}=6.626 \times 10^{-34} \mathrm{Js} \] Type your answer...

Solution

Solution Steps

Step 1: Identify the Relationship Between Energy and Wavelength

The energy of a photon is related to its wavelength by the equation: \[ E = \frac{hc}{\lambda} \] where $ E $ is the energy of the photon, $ h $ is Planck's constant, $ c $ is the speed of light in a vacuum ($3.00 \times 10^8 \, \text{m/s}$), and $ \lambda $ is the wavelength.

Step 2: Rearrange the Equation to Solve for Wavelength

Rearrange the equation to solve for the wavelength $ \lambda $: \[ \lambda = \frac{hc}{E} \]

Step 3: Substitute the Known Values

Substitute the given values into the equation: \[ \lambda = \frac{(6.626 \times 10^{-34} \, \text{Js})(3.00 \times 10^8 \, \text{m/s})}{3.74 \times 10^{-26} \, \text{J}} \]

Step 4: Calculate the Wavelength

Perform the calculation to find the wavelength $ \lambda $.