4. The human eye is a complex sensing device for visible light. The optic nerve needs a minimum of 2.0 x 10-17 J of energy to trigger a series of impulses that eventually reach the brain. (a) How many photons of red light (700.0 nm) are needed? (b) How many photons of blue light (475 nm) are needed? PLEASE POST WORKING OUT AND ANSWER THANKS I AM SO LOST
I'll do my best for the work but you get the answers.
E = hc/wavelength
E = h*c/700E-9.
h is 6.626E-34 J.s
c is 3E8 m/s
This gives the energy of ONE photon of red light. Then
Efrom above x #photons = 2.0E-17
Solve for # photons.
Do the same for the blue light.
(a) Well, let's calculate the energy of one photon of red light using the formula E = hc/λ, where h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3 x 10^8 m/s), and λ is the wavelength of light in meters.
First, let's convert the wavelength of red light from nanometers to meters. We divide 700 nm by 10^9 (since there are 10^9 nm in 1 meter) to get 7 x 10^-7 m.
Now we can plug the values into the formula: E = (6.626 x 10^-34 J·s) * (3 x 10^8 m/s) / (7 x 10^-7 m).
Calculating the energy, we find that one photon of red light has an energy of approximately 2.84 x 10^-19 J.
To find the number of photons needed to reach the minimum energy requirement of 2.0 x 10^-17 J, we divide the required energy by the energy of one photon: (2.0 x 10^-17 J) / (2.84 x 10^-19 J).
Doing the division, we find that approximately 70.4 photons of red light are needed.
(b) Let's repeat the same process for blue light with a wavelength of 475 nm.
Converting the wavelength to meters, we get 475 nm / 10^9 = 4.75 x 10^-7 m.
Using the formula E = hc/λ, we find that one photon of blue light has an energy of approximately 4 x 10^-19 J.
Dividing the required energy (2.0 x 10^-17 J) by the energy of one photon (4 x 10^-19 J), we find that approximately 50 photons of blue light are needed.
So, to summarize:
(a) Approximately 70.4 photons of red light (700 nm) are needed.
(b) Approximately 50 photons of blue light (475 nm) are needed.
Just remember that these calculations are estimates, and actual conditions may vary. Keep your eye on the prize, and I hope this helps lighten up your confusion!
To calculate the number of photons needed, we can use the formula:
Number of photons = Energy required / Energy per photon
(a) For red light with a wavelength of 700.0 nm:
To calculate the energy per photon, we can use the formula:
Energy per photon = hc / λ
Where:
h = Planck's constant = 6.62607015 × 10^-34 J·s
c = speed of light = 2.998 × 10^8 m/s
λ = wavelength in meters
First, convert the wavelength from nanometers to meters:
λ = 700.0 nm = 700.0 × 10^-9 m
Now, calculate the energy per photon:
Energy per photon = (6.62607015 × 10^-34 J·s × 2.998 × 10^8 m/s) / (700.0 × 10^-9 m)
Energy per photon = 2.84718724 × 10^-19 J
Now, we can calculate the number of photons:
Number of photons = (2.0 × 10^-17 J) / (2.84718724 × 10^-19 J)
Number of photons ≈ 70.27 ≈ 70
Approximately 70 photons of red light (700.0 nm) are needed.
(b) For blue light with a wavelength of 475 nm:
First, convert the wavelength from nanometers to meters:
λ = 475 nm = 475 × 10^-9 m
Calculate the energy per photon:
Energy per photon = (6.62607015 × 10^-34 J·s × 2.998 × 10^8 m/s) / (475 × 10^-9 m)
Energy per photon = 4.16840631 × 10^-19 J
Now, calculate the number of photons:
Number of photons = (2.0 × 10^-17 J) / (4.16840631 × 10^-19 J)
Number of photons ≈ 48.00 ≈ 48
Approximately 48 photons of blue light (475 nm) are needed.
To determine the number of photons needed to trigger the optic nerve, we can use the equation:
Energy of a photon = Planck's constant (h) * speed of light (c) / wavelength of light (λ)
(a) Let's calculate the number of photons of red light (700.0 nm) needed.
First, let's convert the wavelength from nanometers (nm) to meters (m):
λ = 700.0 nm = 700.0 x 10^-9 m
Now, we can calculate the energy of a single red photon using the equation mentioned above:
Energy of a photon = (6.626 x 10^-34 J*s) * (3.0 x 10^8 m/s) / (700.0 x 10^-9 m)
Energy of a photon = (19.878 x 10^-26 J*m^2/s) / (700.0 x 10^-9 m)
Energy of a photon = 2.83971 x 10^-17 J
Now, we can determine the number of photons needed by dividing the minimum energy required to trigger the optic nerve by the energy of a single red photon:
Number of photons = Minimum energy required / Energy of a photon
Number of photons = (2.0 x 10^-17 J) / (2.83971 x 10^-17 J)
Number of photons ≈ 0.704
Therefore, approximately 0.704 photons of red light (700.0 nm) are required to trigger the optic nerve.
(b) Let's calculate the number of photons of blue light (475 nm) needed.
First, let's convert the wavelength from nanometers (nm) to meters (m):
λ = 475 nm = 475 x 10^-9 m
Now, we can calculate the energy of a single blue photon using the equation mentioned above:
Energy of a photon = (6.626 x 10^-34 J*s) * (3.0 x 10^8 m/s) / (475 x 10^-9 m)
Energy of a photon = (19.878 x 10^-26 J*m^2/s) / (475 x 10^-9 m)
Energy of a photon = 4.18737 x 10^-17 J
Now, we can determine the number of photons needed by dividing the minimum energy required to trigger the optic nerve by the energy of a single blue photon:
Number of photons = Minimum energy required / Energy of a photon
Number of photons = (2.0 x 10^-17 J) / (4.18737 x 10^-17 J)
Number of photons ≈ 0.478
Therefore, approximately 0.478 photons of blue light (475 nm) are required to trigger the optic nerve.