Question

A) Light with a wavelength of 398.3 nm looks violet. What is the energy, in joules, per photon of this violet light?

b) What is the energy in eV? (1 eV = 1.60217653 ✕ 10−19 J)

Answer 1

A photon of violet light with a wavelength of 398.3 nm has an energy of approximately 4.987 x 10^-19 joules and 3.113 eV.

Step-by-step explanation:

The question asks for the energy per photon of violet light with a wavelength of 398.3 nm and the corresponding energy in electron volts (eV).

To find the energy per photon, we can use the equation E = hf, where E is energy, h is Planck's constant (6.626 x 10-34 J·s), and f is the frequency of the light. Since frequency and wavelength (λ) are related by f = c/λ, where c is the speed of light (3.00 x 108 m/s), we can find the energy of a photon using its wavelength.

Using the provided wavelength (in meters), the energy per photon in joules is calculated as follows:

• E = (6.626 x 10-34 J·s)(3.00 x 108 m/s) / (398.3 x 10-9 m)
• E = 4.987 x 10-19 J

To convert this energy into electron volts, we use the conversion factor 1 eV = 1.602 x 10-19 J.

• E(eV) = (4.987 x 10-19 J) / (1.602 x 10-19 J/eV)
• E(eV) = 3.113 eV

Therefore, a photon of 398.3 nm violet light has an energy of approximately 4.987 x 10-19 J and 3.113 eV.