Question

The equation for photon energy, E , isE=hc/λ where h = 6.626×10^−34 J⋅s (Planck's constant) and c = 2.99×10^8 m/s (the speed of light).What is the wavelength, λ , of a photon that has an energy of E = 4.80×10^−19 J ?Express your answer numerically in meters.Express your answer numerically in meters.

Answer 1

Given:

• Planck's constant, h = 6.626×10⁻³⁴ J⋅s

,

• Speed of light, c = 2.99×10⁸ m/s

,

• Energy = 4.80×10⁻¹⁹ J

Let's find the wavelength of the photon.

Apply the formula for photon energy:

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

Where:

λ is the wavelength.

Rewrite the formula for λ, plug in the values and solve.

We have:

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

Thus, we have:

$\begin{gathered} \lambda=\frac{6.626\times10^{-34}*2.99\times10^8}{4.80\times10^{-19}} \\ \\ \lambda=\frac{1.981174\operatorname{\times}10^{-25}}{4.80\operatorname{\times}10^{-19}} \\ \\ \lambda=4.13\times10^{-7}\text{ m} \end{gathered}$

Therefore, the wavelength of the photon is 4.13 x 10⁻⁷ meters.

• ANSWER:

4.13 x 10⁻⁷ m.