Question

If the visible light spectrum is from 400 to 700 nm, would light with an energy of 2.79 x 10^-19 J be visible with the naked eye? What is the wavelength of this light?

Answer 1

Answer:

713 nm. It is not visible with the naked eye.

Explanation:

Step 1: Given data

• Energy of light (E): 2.79 × 10⁻¹⁹ J

• Planck's constant (h): 6.63 × 10⁻³⁴ J.s

• Speed of light (c): 3.00 × 10⁸ m/s

• Wavelength (λ): ?

Step 2: Calculate the wavelength of the light

We will use the Planck-Einstein equation.

E = h × c / λ

λ = h × c / E

λ = 6.63 × 10⁻³⁴ J.s × 3.00 × 10⁸ m/s / 2.79 × 10⁻¹⁹ J

λ = 7.13 × 10⁻⁷ m

Step 3: Convert "λ" to nm

We will use the relationship 1 m = 10⁹ nm.

7.13 × 10⁻⁷ m × (10⁹ nm/1 m) = 713 nm

This light is not in the 400-700 nm interval so it is not visible with the naked eye.