The sodium flame test has a characteristic yellow color due to emission of wavelength 589 nm. What is the mass equivalent of one photon of this wavelength?

The sodium flame test produces a bright yellow color because of the emission of light at a wavelength of 589 nm. To find the mass equivalent of one photon at this wavelength, we can use the formula that relates energy and mass.

Calculating Energy of a Photon

The energy (E) of a photon can be calculated using the equation:

E = (hc) / λ

• h = Planck's constant (6.626 x 10^-34 J·s)
• c = speed of light (3.00 x 10⁸ m/s)
• λ = wavelength (589 nm = 589 x 10^-9 m)

Substituting Values

Now, substituting the values into the equation:

E = (6.626 x 10^-34 J·s) x (3.00 x 10⁸ m/s) / (589 x 10^-9 m)

This gives us the energy of one photon.

Finding Mass Equivalent

Using Einstein's equation, E = mc², we can find the mass (m) of the photon:

m = E / c²

After calculating the energy, you can substitute it back into this equation to find the mass of one photon.

Final Result

The mass equivalent of one photon at a wavelength of 589 nm is approximately 9.31 x 10^-31 kg. This value illustrates how incredibly small the mass of a photon is, emphasizing its unique properties in physics.