How much energy is emitted by 9.4 mg of sodium atoms emitting light at a wavelength of 5.8E-7 m? Answer in units of J.

Question

How much energy is emitted by 9.4 mg of sodium atoms emitting light at a wavelength of 5.8E-7 m? Answer in units of J.

Answer 1

E = hc/λ

E = energy of 1 photon of light

h = Planck's constant = 6.626x10^-34 J-sec

c = speed of light = 3x10⁸ m/sec

λ = wavelength = 5.8x10^-7 m

E = (6.626x10^-34 J-sec)(3x10⁸ m/sec) / 5.8x10^-7 m

E = 3.43x10^-19 J ... This is the energy from 1 photon of light from 1 atom of Na

We must find the number of photons from 9.4 mg Na atoms:

9.4 mg Na x 1 g / 1000 mg x 1 mol Na / 23 g x 6.02x10²³ atoms / mole = 2.46x10²⁰ atoms of Na

3.43x10^-19 J/photon x 2.46x10²⁰ photons = 84.4 J = energy from 9.4 mg Na atoms