2. The retina of a human eye can detect light when radiant energy incident on it is at least 4.0X10-17 J. For light of 600-nm wavelength, how many photons does this correspond to?
Well, buckle up because we're about to go on a quantum physics rollercoaster!
To find out the number of photons, we need to use the equation E = hf, where E is the energy of a photon, h is Planck's constant (approximately 6.63×10^-34 J·s), and f is the frequency of the light.
Now let's convert the wavelength to frequency using the equation f = c/λ, where c is the speed of light (approximately 3.00×10^8 m/s) and λ is the wavelength.
So, f = (3.00×10^8 m/s) / (600×10^-9 m) which gives us a frequency of 5.00×10^14 Hz.
Now let's calculate the energy of one photon using E = hf. Substituting the values, we get E = (6.63×10^-34 J·s) × (5.00×10^14 Hz) = 3.32×10^-19 J.
Finally, to find the number of photons, we divide the total energy (4.0×10^-17 J) by the energy of one photon (3.32×10^-19 J).
(4.0×10^-17 J) / (3.32×10^-19 J) ≈ 1.20×10^2 photons.
So, it takes approximately 120 photons of 600-nm wavelength light to make the retina of a human eye yell, "I see the light!"
To find the number of photons corresponding to the given energy, we can use the formula:
Number of photons = Energy / Energy per photon
First, we need to calculate the energy per photon using the formula:
Energy per photon = (Planck's constant x speed of light) / wavelength
Planck's constant (h) = 6.62607015 x 10^-34 J s
Speed of light (c) = 3.00 x 10^8 m/s
Wavelength (λ) = 600 nm = 600 x 10^-9 m
Plugging in these values, we can calculate the energy per photon:
Energy per photon = (6.62607015 x 10^-34 J s x 3.00 x 10^8 m/s) / (600 x 10^-9 m)
= (1.987822 x 10^-25 J) / (600 x 10^-9 m)
≈ 3.313037 x 10^-17 J
Now, we can calculate the number of photons using the given energy:
Number of photons = 4.0 x 10^-17 J / (3.313037 x 10^-17 J)
≈ 1.2072 photons
Therefore, for light of 600-nm wavelength and an incident energy of 4.0 x 10^-17 J, this corresponds to approximately 1.2072 photons.
To determine the number of photons corresponding to a given amount of energy, you can use the equation:
E = N * h * c / λ
Where:
E is the energy of the photons,
N is the number of photons,
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 of light.
We know the energy threshold E (4.0 x 10^-17 J) and the wavelength λ (600 nm = 600 x 10^-9 m). Let's substitute these values into the equation and solve for N:
4.0 x 10^-17 J = N * (6.626 x 10^-34 J·s) * (3.00 x 10^8 m/s) / (600 x 10^-9 m)
Simplifying the equation:
4.0 x 10^-17 J = N * (6.626 x 10^-34 J·s * 3.00 x 10^8 m/s) / (600 x 10^-9 m)
Now, let's cancel out the units and compute the result:
4.0 x 10^-17 J = N * (6.626 x 3.00) / (600 x 10^-9)
4.0 x 10^-17 J = N * (19.878 x 10^-26) / (600 x 10^-9)
4.0 x 10^-17 J = N * 3.313 x 10^-17
Now, rearranging the equation to solve for N:
N = (4.0 x 10^-17 J) / (3.313 x 10^-17)
N = 1.207
Thus, for light of 600 nm wavelength, the number of photons that correspond to an energy of at least 4.0 x 10^-17 J is approximately 1.207 photons.
Photon energy = h*c/(wavelength)
= 6.62*10^-34 J*s * (3*10^8 m/s)/600*10^-9 m = 3.3*10^-19 J
4*10^-17 J corresponds to 120 photons of that color (orange) light