Question

4. (5pt) Below is the spectrum of our sun measured at the earth's surface: 14 1.2 1.0 0.8 0.6 0.4 0.2 0.0 400 600 800 1000 Wavelength (nm) a. At approximately what wavelength is the sun's irradiance at a maximum? Human eyesight is centered in the green region of the spectrum; is this a coincidence? Spectral Irradiance

Answer 1

1) According to the diagram, the sun's irradiance is maximum at around 500 nm ( green region ). The human eye can detect 340 to 780 nm. So we can say that human eyesight is centered at 520-560 nm, which is also the green region. This is a pure coincidence.

2) The energy of a photon is given by   $E = hc/\lambda$  

where h is Planck's constant = 6.62 x 10^-34 J.s.

c is speed of light = 2.99 x 10⁸ m/s². and $\lambda$ is the wavelength.

So a photon with wavelength 1000 nm has energy =  (6.62 x 10^-34 J.s. x   2.99 x 10⁸ m/s²) / 1000 x 10^-9 m

= 1.987 x 10^-19 Joules.

A photon of wavelength 1000 nm lies in the infrared region.

3) For wavelength = 500 nm, Energy must be double that of previous, as wavelength is in the denominator. So Energy corresponds to 3.975 x 10^-19 Joules. Light corresponding to 500 nm has double the energy of light corresponding to 1000 nm.

4) Light corresponding to 300 nm is in the Ultraviolet (UV) region. And we know that the earth's stratosphere has a layer of ozone ( O₃ ) that absorbs the UV light. Hence, UV light is missing at earth's surface.