Light is shining perpendicularly on the surface of the earth with an intensity of 680 W/m2. Assuming that all the photons in the light have the same wavelength (in vacuum) of 478 nm, determine the number of photons per second per square meter that reach the earth.

Energy =Power x time =680 W/m2 x 1 second =680 Joule/m2

Energy of 1 photone = hf =hc/λ
Number of photones =Energy/energy of 1 photon =
N=680• λ/hc=680•478•10⁻⁹/6.63•10⁻³⁴•3•10⁸=…

Thank You So much

To determine the number of photons per second per square meter that reach the earth, you can use the formula:

Number of photons per second per square meter = Intensity of light / Energy per photon

First, let's convert the given wavelength from nanometers (nm) to meters (m):

Wavelength = 478 nm = 478 × 10^(-9) m

The energy per photon can be calculated using the formula:

Energy per photon = Planck's constant (h) × speed of light (c) / wavelength

Planck's constant (h) = 6.626 × 10^(-34) J·s (joule-seconds)
Speed of light (c) = 3.00 × 10^8 m/s

Now, substitute the values into the formula:

Energy per photon = (6.626 × 10^(-34) J·s) × (3.00 × 10^8 m/s) / (478 × 10^(-9) m)

Next, calculate the intensity of light in watts per square meter (W/m^2):

Intensity of light = 680 W/m^2

Now, divide the intensity of light by the energy per photon to find the number of photons per second per square meter:

Number of photons per second per square meter = (680 W/m^2) / (Energy per photon)

Calculating the energy per photon:

Energy per photon = (6.626 × 10^(-34) J·s) × (3.00 × 10^8 m/s) / (478 × 10^(-9) m) = 4.129 × 10^(-19) J

Finally, substitute the value of the energy per photon into the previous formula:

Number of photons per second per square meter = (680 W/m^2) / (4.129 × 10^(-19) J)

Calculating the final answer:

Number of photons per second per square meter = 1.646 × 10^21 photons/m^2/s

Therefore, approximately 1.646 × 10^21 photons per second per square meter reach the earth.

To determine the number of photons per second per square meter that reach the earth, we can use the formula:

Number of photons = Power / Energy per photon

First, we need to find the energy per photon using the formula:

Energy per photon = Planck's constant * speed of light / wavelength

Planck's constant (h) = 6.626 x 10^-34 J*s
Speed of light (c) = 3 x 10^8 m/s
Wavelength (λ) = 478 nm = 4.78 x 10^-7 m

Calculating the energy per photon:

Energy per photon = (6.626 x 10^-34 J*s) * (3 x 10^8 m/s) / (4.78 x 10^-7 m)

Next, we can determine the number of photons per second per square meter using the formula:

Number of photons = Intensity of light / Energy per photon

Intensity of light = 680 W/m^2

Calculating the number of photons:

Number of photons = (680 W/m^2) / (Energy per photon)

Now, let's substitute the values and calculate:

Energy per photon = (6.626 x 10^-34 J*s) * (3 x 10^8 m/s) / (4.78 x 10^-7 m)

Number of photons = (680 W/m^2) / (Energy per photon)

After performing the calculations, you will have the number of photons per second per square meter that reach the earth.