Question

Calculate the energy of a photon of electromagnetic radiation at a wavelength of 488.0 nm (wavelength of an argon laser).

a) 4.08 x 10⁻¹⁹ J
b) 3.88 x 10⁻¹⁹ J
c) 4.35 x 10⁻¹⁹ J
d) 3.72 x 10⁻¹⁹ J

Answer 1

The energy of a photon of electromagnetic radiation at a wavelength of 488.0 nm is calculated using the equation E = hc / λ. After converting the wavelength to meters and applying the constants for Planck's constant and the speed of light, the energy is found to be 4.08 × 10-19 J.

Step-by-step explanation:

To calculate the energy of a photon of electromagnetic radiation with a given wavelength, you can use the equation:

E = hc / λ

Where:

E is the energy of the photon in joules (J)

h is Planck's constant (6.626 × 10-34 J·s)

c is the speed of light in a vacuum (3.00 × 108 m/s)

λ is the wavelength of the photon in meters (m)

First, we need to convert the given wavelength from nanometers to meters:

488.0 nm = 488.0 × 10-9 m

Then, we use the equation to find the energy:

E = (6.626 × 10-34 J·s) (3.00 × 108 m/s) / (488.0 × 10-9 m)

E = (6.626 × 10-34 × 3.00 × 108) / 488.0 × 10-9

E = 4.08 × 10-19 J

So, the correct answer is:

a) 4.08 × 10-19 J