What is the energy of a photon of red light having a frequency of 5.16 ✕ 1014 Hz?

Question

What is the energy of a photon of red light having a frequency of 5.16 ✕ 10¹⁴ Hz?

Answer 1

The relationship you need is: E = hν where E is energy (J), h is Planck's constant (6.626 x 10^–34 J•s), and ν (Greek letter "nu") is frequency (s^–1, also called Hz).

Given: ν = 5.16 x 10¹⁴ Hz

Asked: E = ?

Substitute the values for ν and Planck's constant and do the math:

E = (6.626 x 10^–34 J•s)(5.16 x 10¹⁴ Hz) = answer in Joules

Answer 2

Since this equation gives the number for Hertz and also tells you the color of the photon, it is actually giving you two of the three variables. Within the visible light spectrum, red is typically 700 nanometers (this is your wavelength).

The speed of light, or C, = 299,792,458 m/s

Therefore... (299,792,458 m/s x 5.16*10^14 Hz) / 700 nm = E of the photon = 2.2098986904...*10^20

The answer should have 3 significant digits because 5.16 has 3 significant digits, so the answer should be (rounded) 2.21*10^20 Joules (J).

In general, you'll find that violet/blue side of the spectrum has more energy than the red side because the spectrum increases in wavelength as it moves from the violet/blue end to the red end. Diving by a smaller number (the violet/blue end) gives you a larger answer, or a greater value for E, and diving by a larger number (the red end) gives you a smaller answer, or a smaller value for E.