"your eyes receive a signal consisting of blue light, 470nm. The energy of the signal is 2.5*10^-14J. How many photons reach your eyes?"
The energy per photon is Planck's Constant x speedlight/wavelenght.
then number of photons= totalenergy/energy per photon
To calculate the number of photons that reach your eyes from a signal with blue light of 470 nm and an energy of 2.5 x 10^-14 J, we can use the equation:
E = N * h * c / λ
Where:
E = energy of the signal (2.5 x 10^-14 J)
N = number of photons
h = Planck's constant (6.626 x 10^-34 J*s)
c = speed of light (3 x 10^8 m/s)
λ = wavelength of the light (470 nm = 470 x 10^-9 m)
Rearranging the equation to solve for N, we have:
N = E / (h * c / λ)
Substituting the given values, we get:
N = (2.5 x 10^-14 J) / ((6.626 x 10^-34 J*s * 3 x 10^8 m/s) / (470 x 10^-9 m))
N = (2.5 x 10^-14 J) * ((470 x 10^-9 m) / (6.626 x 10^-34 J*s * 3 x 10^8 m/s))
N = (2.5 x 10^-14 J) * (7.1 x 10^14)
N = 17.75
Therefore, approximately 17.75 photons reach your eyes.
To determine the number of photons that reach your eyes, you need to use the equation:
Energy of a single photon = Planck's constant (h) * speed of light (c) / wavelength
Given:
Energy of the signal (E) = 2.5 * 10^-14 J
Wavelength (λ) = 470 nm = 470 * 10^-9 m
First, we need to convert the wavelength from nanometers (nm) to meters (m):
470 nm = 470 * 10^-9 m
Now, we can substitute the values into the equation and solve for the energy of a single photon:
Energy of a single photon = (Planck's constant * speed of light) / wavelength
Energy of a single photon = (6.626 × 10^-34 J·s * 3.00 × 10^8 m/s) / (470 * 10^-9 m)
Energy of a single photon = (1.9883 × 10^-25 J*m) / (470 * 10^-9 m)
Energy of a single photon = 4.23 × 10^-19 J
Now, to calculate the number of photons:
Number of photons = Total energy of the signal / Energy of a single photon
Number of photons = (2.5 * 10^-14 J) / (4.23 × 10^-19 J)
Number of photons = 5.92 × 10^4 photons
Therefore, approximately 5.92 × 10^4 photons reach your eyes.