Question

A laser pointer emits red light with a wavelength of 690 nm. What is the energy of a photon of this light?

A) 2.87 × 10⁻¹⁹ J
B) 3.03 × 10⁻¹⁹ J
C) 2.87 × 10⁻²⁰ J
D) 3.03 × 10⁻²⁰ J

Answer 1

The energy of a photon of red light with a wavelength of 690 nm is 2.87 x 10^-19 Joules, calculated using Planck's formula.

Step-by-step explanation:

To find the energy of a photon with a given wavelength, we use the formula:

E = h \(\frac{c}{\lambda}\)

Where E is the energy of the photon, h is Planck's constant (6.626 x 10-34 Joule seconds), c is the speed of light in a vacuum (3.00 x 108 m/s), and \(\lambda\) is the wavelength of the light. In this case, the wavelength (\(\lambda\)) is given as 690 nm, which is 690 x 10-9 meters.

First, convert the wavelength to meters:

690 nm = 690 x 10-9 m

Then, plug the values into the energy formula and calculate:

E = (6.626 x 10-34 J s) (3.00 x 108 m/s) / (690 x 10-9 m)

The energy E is approximately 2.87 x 10-19 Joules.

Therefore, the energy of a photon of red light with a wavelength of 690 nm is 2.87 \(\times\) 10-19 J (Option A).