Question

A lithium flame has a characteristic red color due to emissions of wavelength 671 nm. What is the mass equivalence of 1 mol of photons of this wavelength (1 J = 1 kg·m²/s²)?

Answer 1

Answer:

1.98x10⁻¹² kg

Explanation:

The energy of a photon is given by:

• E= hc/λ

h is Planck's constant, 6.626x10⁻³⁴ J·s

c is the speed of light, 3x10⁸ m/s

and λ is the wavelenght, 671 nm (or 6.71x10⁻⁷m)

• E = 6.626x10⁻³⁴ J·s * 3x10⁸ m/s ÷ 6.71x10⁻⁷m = 2.96x10⁻¹⁹ J

Now we multiply that value by Avogadro's number, to calculate the energy of 1 mol of such protons:

• 1 mol =  6.023x10²³ photons

• 2.96x10⁻¹⁹ J *  6.023x10²³ = 1.78x10⁵ J

Finally we calculate the mass equivalence using the equation:

• E=m*c²

• m=E/c²

• m =  1.78x10⁵ J / (3x10⁸ m/s)² = 1.98x10⁻¹² kg