Math Snap

STEP 1

Assumptions1. The energy of the photon is $6.89 \times10^{-19} \mathrm{~J}$
. We are to find the wavelength of the photon3. We will use the Planck-Einstein relation, which states that the energy of a photon is given by the product of Planck's constant (h) and the speed of light (c), divided by the wavelength of the photon (λ). The equation is $= \frac{hc}{\lambda}$, where is the energy of the photon, h is Planck's constant ($6.63 \times10^{-34} \mathrm{~J \cdot s}$), c is the speed of light ($3.00 \times10^{8} \mathrm{~m/s}$), and λ is the wavelength of the photon.
4. We will rearrange the equation to solve for λ.

STEP 2

First, we need to rearrange the Planck-Einstein relation to solve for λ.
$$\lambda = \frac{hc}{}$$

STEP 3

Now, plug in the given values for Planck's constant (h), the speed of light (c), and the energy of the photon () to calculate the wavelength.
$$\lambda = \frac{(6.63 \times10^{-34} \mathrm{~J \cdot s}) \times (3.00 \times10^{8} \mathrm{~m/s})}{6.89 \times10^{-19} \mathrm{~J}}$$

Calculate the wavelength of the photon.
$$\lambda = \frac{(6.63 \times10^{-34} \mathrm{~J \cdot s}) \times (3.00 \times10^{8} \mathrm{~m/s})}{6.89 \times10^{-19} \mathrm{~J}} =2.88 \times10^{-7} \mathrm{~m}$$The wavelength of the photon is $2.88 \times10^{-7} \mathrm{~m}$.