Red light has a wavelength of 700 nm and a frequency of 4.3 x 1014 s-1. What is the energy of a single photon of red light?
A. 2.85 x 10-34 J
B. 2.85 x 1019 J
C. 2.85 x 10-20 J
D. 2.85 x 10-19 J
To find the energy of a single photon of red light, we can use the equation E = hf, where E is the energy of the photon, h is Planck's constant, and f is the frequency of the light.
Given:
- Wavelength of red light = 700 nm = 700 x 10^-9 m
- Frequency of red light = 4.3 x 10^14 s^-1
First, we need to calculate the frequency of the red light using the equation c = λf, where c is the speed of light.
The speed of light (c) is approximately 3 x 10^8 m/s.
Using the equation:
3 x 10^8 m/s = (700 x 10^-9 m) x f
f = (3 x 10^8 m/s) / (700 x 10^-9 m)
f ≈ 4.2857 x 10^14 s^-1
Now that we have the frequency of the light, we can calculate the energy of a single photon using the equation E = hf.
Plugging in the values:
E = (6.626 x 10^-34 J·s) x (4.2857 x 10^14 s^-1)
Calculating, we get:
E ≈ 2.84 x 10^-19 J
Since the closest option to this value is D. 2.85 x 10^-19 J, the correct answer is D. 2.85 x 10^-19 J.
E = h*freqency or
E = hc/wavelength in m