A waveband of light has a wavelength of 1100 nanometers. How much energy is in a single photon of this light?
a. 9.9 x 10^-32 J
b. 7.2 x 10^-40 J
c. 7.0 x 10^-45 J
d. 1.4 x 10^-38 J
Using the equation E = hc/λ, where h is Planck's constant (6.626 x 10^-34 J s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength in meters, we can find the energy in a single photon:
E = hc/λ = (6.626 x 10^-34 J s) x (3.00 x 10^8 m/s) / (1100 x 10^-9 m)
E = 1.81 x 10^-19 J
Therefore, the energy in a single photon of light with a wavelength of 1100 nanometers is a. 9.9 x 10^-32 J.
Well, first of all, let me just say that photons are pretty energetic little fellas! Now, to calculate the energy of a photon, we can use the equation E = hc/λ, where E is the energy, h is Planck's constant (approximately 6.626 x 10^-34 J·s), c is the speed of light (approximately 3.00 x 10^8 m/s), and λ is the wavelength.
So, plugging in the numbers, we get E = (6.626 x 10^-34 J·s)(3.00 x 10^8 m/s)/(1100 x 10^-9 m). After doing the math, we find that the energy of a single photon of this light is approximately 5.70 x 10^-19 J.
But wait, none of the given options match this answer! Oh no! Looks like the options are playing hide-and-seek with the correct answer. Well, in that case, I'll just have to create option (e) "None of the above." Trust your math skills and choose the right answer that isn't afraid to be unique!
To calculate the energy of a single photon, you can use the equation E = hf, where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J·s), and f is the frequency of the light.
First, convert the wavelength of the light from nanometers to meters. Since 1 meter is equal to 1 x 10^9 nanometers, divide the wavelength by 1 x 10^9 to get the wavelength in meters:
1100 nm / (1 x 10^9 nm/m) = 1.1 x 10^-6 m
Now, calculate the frequency of the light using the equation f = c/λ, where c is the speed of light (3 x 10^8 m/s) and λ is the wavelength:
f = (3 x 10^8 m/s) / (1.1 x 10^-6 m) ≈ 2.73 x 10^14 Hz
Finally, substitute the values of h and f into the equation E = hf:
E = (6.626 x 10^-34 J·s) * (2.73 x 10^14 Hz) ≈ 1.81 x 10^-19 J
Therefore, the energy in a single photon of this light is approximately 1.81 x 10^-19 J. None of the given answer choices match this value, so none of the options are correct.
To calculate the energy of a single photon, you can use the equation:
E = hf
where E is the energy of the photon, h is the Planck's constant (approximately 6.626 x 10^-34 Joule-seconds), and f is the frequency of the waveband.
First, you need to find the frequency of the waveband. To do this, you can use the equation:
c = λf
where c is the speed of light (approximately 3.0 x 10^8 meters per second), λ is the wavelength of the waveband, and f is the frequency.
Rearranging the equation, we get:
f = c / λ
Substituting the given values:
f = (3.0 x 10^8 m/s) / (1100 x 10^-9 m)
f = 2.73 x 10^14 Hz
Now that we have the frequency, we can calculate the energy of a single photon:
E = hf = (6.626 x 10^-34 J.s) * (2.73 x 10^14 Hz)
E = 1.80798 x 10^-19 J
Round this value to the appropriate number of significant figures, and we find that the energy of a single photon of this light is approximately 1.81 x 10^-19 J.
Therefore, the closest answer choice is d. 1.4 x 10^-38 J.