What is the wavelength of a photon that has an energy of #4.41 x 10^-19#?

Question

Serenity Allen · Accepted Answer

What unit of energy are you using? I assume it's J...? In which case its about 4.5 x #10^-7# m

If you use Planck-Einstein equation, E = h.f where h is Planck's constant, which 6.626 x #10^-34# J.s, then you can work out the frequency: f = E/h, = 4.41 x #10^-19#/6.626 x #10^-34# = 6.655 x #10^14# Hz. Then convert frequency to wavelength using #lambda# = c/f where c is the speed of light, 3 x #10^8# m/sec. #lambda# = 3 x #10^8# / 6.655 x #10^14# = 4.51 x #10^-7# m.

Owen Ambrose · Answer

undefined To find the wavelength of a photon with a given energy, you can use the equation:

$$E = \dfrac{hc}{\lambda}$$

where:
- $E$ is the energy of the photon,
- $h$ is Planck's constant ($6.626 \times 10^{-34} \, \text{J} \cdot \text{s}$),
- $c$ is the speed of light in a vacuum ($3.00 \times 10^8 \, \text{m/s}$),
- $\lambda$ is the wavelength of the photon.

Rearranging the equation to solve for wavelength, you get:

$$\lambda = \dfrac{hc}{E}$$

Plugging in the values given:

$$\lambda = \dfrac{(6.626 \times 10^{-34} \, \text{J} \cdot \text{s}) \times (3.00 \times 10^8 \, \text{m/s})}{4.41 \times 10^{-19} \, \text{J}}$$

Solving this equation will give you the wavelength of the photon.