Find the energy of a photon of light if the wavelength is 4.60x10^-7 m.

Answer 1

I'd like to add to the answer provided by @Anthony P. He has shown calculations using ergs and electron volts. Many instructors/text books use Joules, so here is the calculation in joules.

E = hc/λ

E = energy = ?

h = Plank's constant = 6.626x10^-34 Jsec

c = speed of light = 3x10⁸ m/sec

λ = wavelength = 4.60x10^-7 m

Solving for E, we have...

E = (6.626x10^-34 Jsec)(3x10⁸ m/sec) / 4.60x10^-7 m

E = 4.32x10^-19 J

You can convert this to ergs to check the previous answer:'

1 erg = 1x10^-7 joules

4.32x10^-19 J x 1 erg / 1x10^-7 J = 4.32x10^-12 ergs

Answer 2

Find the energy of a photon of light if the wavelength is 4.60x10^-7 m.

Photon energy is given by E = h*c / λ

h = 6.62 E -27 erg*sec (from a table of constants)

c = 3.00 E+10 cm/sec

λ = 4.60 E-7 m * 100 cm/m = 4.60 E-5 cm

E = (6.62*3/4.60) E(-27+10+5) = 4.32 E-12 erg

Sometimes, photon energies are expressed in electron volts (especially for high energy rays)

E = 4.32 E-12 ergs * 6.24 E+11 eV/erg = 2.70 eV

Note that the wavelength is also often given in nanometers for visible light.

λ = 4.60 E-7 m * 1E+9 nm/m = 460 nm, which is the color of blue light,