Question

A photon has a wavelength of 781 nm. Calculate the energy of the photon in joules. Enter your answer in scientific notation.

Answer 1

Answer:

E = 2.54 e(-25)

Explanation:

For this calculation we will use the Planck formula on the dual wave corpuscle of light, which relates the energy of the photon with the frequency from the Planck constant, whose value is 6,626 · 10 ^ (- 34) J · s. Planck's formula is E = h · v, where E is the energy, h the Planck constant and v the frequency (Hz or s-1).

First and according to Einstein who established in his 1905 article on the Special Theory of Relativity, light always has the same speed: 300,000,000 meters per second in a vacuum. This means that you can convert from nanometers of wavelength to frequency with ease. Simply divide the speed by the wavelength in meters. Because your wavelength is in nanometers, multiply it by one billion to get the result in hertz.

So:

(300.000.000 m/s) / 781 nm = 384,122.919

384,122.919 * 1,000,000 = 384,122,919,334.18 Hz (or s^-1)

Now we apply the Plank equation

E = h * v

E = 6,626 · 10 ^ (- 34) J*s * 384,122,919,334.18 s^-1

E = 2.54 e(-25)

Answer 2

The energy of a photon that has a wavelength of 781nm is calculated to be 2.55 × 10-¹⁹ J.

How to calculate energy of a photon?

The energy of a photon can be calculated using the following formula:

E = hc/λ

Where;

• E = energy in joules
• h = Planck's constant = 6.626 × 10-³⁴J/s
• c = speed of light = 3 × 10⁸m/s
• λ = wavelength= 781nm = 7.81 × 10-⁷m

E = 6.626 × 10-³⁴ × 3 × 10⁸/7.81 × 10-⁷

E = 19.88 × 10-²⁶ ÷ 7.81 × 10-⁷

E = 2.55 × 10-¹⁹ J

Therefore, energy of a photon that has a wavelength of 781nm is calculated to be 2.55 × 10-¹⁹J.

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