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What is the wavelength of a wave with energy equal to 1.528 x 10-13 J? E=hc/LaTeX: \lambdaλ Energy= Measured in Joules h=Plank's constant, 6.626 x 10-34 J x s c=speed of light, 3.00 x108 m/s LaTeX: \lambdaλ= wavelength in meters Group of answer choices 1.301 x 1029 m 6.918 x 1028m 6.918 x 10-13m 1.301 x 10-12m

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dsdrajlin

Answer:

1.301 × 10⁻¹² m

Explanation:

Step 1: Given and required data

  • Energy of the electromagnetic wave (E): 1.528 × 10⁻¹³ J
  • Planck's constant (h): 6.626 × 10⁻³⁴ J . s
  • Speed of light (c): 3.00 × 10⁸ m/s

Step 2: Calculate the wavelength (λ) of the electromagnetic wave

We can calculate the wavelength of the electromagnetic wave using the Planck-Einstein's relation.

E = h × c / λ

λ = h × c / E

λ = (6.626 × 10⁻³⁴ J . s) × (3.00 × 10⁸ m/s) / 1.528 × 10⁻¹³ J

λ = 1.301 × 10⁻¹² m

Lanuel

The wavelength of this wave is equal to: D. [tex]1.301 \times 10^{-12}\;meter[/tex]

Given the following data:

  • Energy = [tex]1.528 \times 10^{-13} \;Joules[/tex]
  • Plank's constant = [tex]6.626 \times 10^{-34}\;Js[/tex]
  • Speed of light = [tex]3 \times 10^8\;m/s[/tex]

To determine the wavelength of this wave, we would apply Einstein's equation for photon energy:

Mathematically, Einstein's equation for photon energy is given by the formula:

[tex]E=\frac{hc}{\lambda}[/tex]

Where:

  • E is the energy.
  • h is Plank's constant.
  • [tex]\lambda[/tex] is the wavelength.
  • c is the speed of light.

Making [tex]\lambda[/tex] the subject of formula, we have:

[tex]\lambda = \frac{hc}{E}[/tex]

Substituting the given parameters into the formula, we have;

[tex]\lambda = \frac{6.626 \times 10^{-34}\; \times \;3.0 \times 10^{8}}{1.528 \times 10^{-13} }\\\\\lambda = \frac{1.99 \times 10^{-25}}{1.528 \times 10^{-13} }\\\\\lambda =1.301 \times 10^{-12}\;meter[/tex]

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