Question

What is the energy for a wavelength of 486nm?

a) 2.54 eV
b) 3.00 eV
c) 4.07 eV
d) 5.18 eV

Answer 1

The energy of a photon with a wavelength of 486 nm is closest to 2.54 eV, which makes option a the correct answer when compared to the given choices.

Step-by-step explanation:

To find the energy of a photon with a wavelength of 486 nm, we use the equation E = hf where E is the energy, h is Planck's constant (6.62607015 × 10−19 J·s), and f is the frequency. Since frequency and wavelength (λ) are related by f = c/λ, where c is the speed of light (3 × 108 m/s), we can combine the two equations to derive E = hc/λ. Substituting the values, E = (6.62607015 × 10−19 J·s)(3 × 108 m/s) / (486 × 10−9 m). To convert the energy from joules to electronvolts, we use the conversion factor 1 eV = 1.602 × 10−19 J, which results in an energy slightly above option c, roughly 2.54 eV according to actual computations. Therefore, option a is the closest among the given options.