Two members of the Boron family owe their names to bright lines in their emission spectra. Indium has a bright indigo blue line (451.1nm) and Thallium has a bright green line (535.0 nm).

What are the energies of these two spectra lines?

E Indium = 4.407 x 10⁻¹⁹ J

E Thallium = 3.716 x 10⁻¹⁹ J

Explanation:

From Planck's equation for a given wavelength, the energy is given by.

E = h (c / λ)

h: Planck's constant, 6.626 x 10⁻³⁴ J·s

c: light speed, 3 x 10⁸ m/s

λ: wavelength in m

We will need first to convert the given wavelengths to m:

451.1 nm x (1 m/10⁹ nm) = 4.511 x 10⁻⁷ m

535.0 nm x (1 m/10⁹ nm) = 5.350 x 10⁻⁷ m

E Indium = 6.626 x 10⁻³⁴ J·s x 3x 10 ⁸ m/s / 4.511 x 10⁻⁷ m = 4.407 x 10⁻¹⁹ J

E Thallium = 6.626 x 10⁻³⁴ J·s x 3x 10 ⁸ m/s / 5.350 x 10⁻⁷ m = 3.716 x 10⁻¹⁹ J