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 521 nm, determine the number of photons per second per square meter that reach the earth.

To determine the number of photons per second per square meter that reach the earth, we will use the intensity of light and the energy of each photon.

Step 1: Convert the intensity of light from watts per square meter (W/m2) to energy per second per square meter (J/s.m2).
- 1 watt (W) = 1 joule/second (J/s)
- The intensity of light is given as 680 W/m2.
- Therefore, the energy per second per square meter (J/s.m2) is also 680 J/s.m2.

Step 2: Calculate the energy of each photon using the given wavelength.
- The energy of a single photon is given by the equation E = hc/λ, where E is the energy, h is Planck's constant (6.626 × 10^-34 J.s), c is the speed of light in a vacuum (3.00 × 10^8 m/s), and λ is the wavelength.
- Substituting the given values, we have E = (6.626 × 10^-34 J.s × 3.00 × 10^8 m/s) / (521 × 10^-9 m).
- Calculating this expression, we get E ≈ 3.85 × 10^-19 J.

Step 3: Determine the number of photons per second per square meter by dividing the energy per second per square meter by the energy of each photon.
- Divide 680 J/s.m2 (energy per second per square meter) by 3.85 × 10^-19 J (energy of each photon).
- The units cancel out, leaving us with the number of photons per second per square meter.
- The result is approximately 1.77 × 10^21 photons/s.m2.

Therefore, approximately 1.77 × 10^21 photons per second per square meter reach the earth's surface.

To determine the number of photons per second per square meter that reach the earth, you need to know the energy carried by a single photon.

The energy of a photon can be calculated using the equation:

E = hc/λ

Where:
- E is the energy of the photon
- h is Planck's constant (6.63 x 10^-34 J*s)
- c is the speed of light in a vacuum (3 x 10^8 m/s)
- λ is the wavelength of the photon

In this case, the wavelength (λ) is given as 521 nm, which can be converted to meters by dividing by 1,000,000:

λ = 521 nm / 1,000,000 = 5.21 x 10^-7 m

Now, substitute the values into the equation to calculate the energy of a single photon:

E = (6.63 x 10^-34 J*s * 3 x 10^8 m/s) / (5.21 x 10^-7 m)
E ≈ 3.8 x 10^-19 J

The intensity of the light is given as 680 W/m^2, which represents the energy per second per square meter reaching the earth's surface.

To calculate the number of photons per second per square meter, divide the intensity (in watts) by the energy of a single photon (in joules):

Number of photons = 680 W/m^2 / (3.8 x 10^-19 J)
Number of photons ≈ 1.79 x 10^21 photons/s/m^2

Therefore, approximately 1.79 x 10^21 photons per second per square meter reach the earth's surface.