Question

What would the wavelength of maximum be for infrared radiation from the surface of Mercury?
ranges from ____  nm to ____  nm

What about for the moon?
ranges from _______  nm to _______  nm

Answer 1

The electromagnetic spectrum is the range of all possible wavelengths of electromagnetic radiation, ranging from high energy gamma rays through visible light and down to low energy radio waves. Infrared covers everything above what we can see with our eyes, which is approximately 700nm, although humans can detect light up to slightly more than 1300nm if the intensity is sufficient. People are particularly good at seeing infra-red up to around 900nm.

Since Mercury has less mass than Earth, the surface gravity on Mercury is less than the surface gravity on Earth. The surface gravity on Mercury is only about 38% of the surface gravity on Earth, so if you weigh 100 pounds on Earth, you would weigh only 38 pounds on Mercury.

Wavelength of photon changes as it rises from a planet's surface.

The setup assumes a large mass(Earth?) an a photon launched from its surface initially. The wavelength of the photon on launch is known. Then the new energy of the photon is compared with energy it traveled a distance d.

Initially,

E₁=(GMm /R)+1/2 * mv²

where m- mass of photon, M is mass of earth, R is radius. Finally

E₂=GMx/ (R+d)+1/2 * xv²

where x is new mass of the photon. Putting m=h / Lc, L is wavelength

Plancks constant h = 6.626176 x 10^-34 joule-seconds.

We know wavelength of infrared radiation ranges from 700 nm to 1300 nm in Earth it is enough to confirm infrared wavelength based on mercury new mass which 38% of earth.

Therefore Lc = 6.626176 x 10^-34 * 0.38 / 700 * 10^-9 = 0.36 x 10^-27 metres = 3.6 x 10^-19 nm

also Lc = 6.626176 x 10^-34 * 0.38 / 1300 * 10^-9 = 0.194 x 10^-27 metres = 1.94 x 10 ^-19 nm

The moon's mass is 7.35 x 10²² kg, about 1.2 percent of Earth's mass. Put another way, Earth weighs 81 times more than the moon.

We know wavelength of infrared radiation ranges from 700 nm to 1300 nm in Earth. As moons mass is 0.012 % of Earth, it is enough to confirm infrared wavelength based on moons mass.

Therefore Lc = 6.626176 x 10^-34 * 0.012 / 700 * 10^-9 = 1.136 x 10^-31 metres = 1.136 x 10^-22 nm

also Lc = 6.626176 x 10^-34 * 0.012 / 1300 * 10^-9 = 0.194 x 10^-27 metres = 6.116 x 10 ^-22 nm.

The rest is the original calculation of the Wavelength radiations

Let the new wavelength be W.

We can equate the 2: (GMh/RLc) + 1/2 (h/L)²=GMh / (R+d)Wc+1 / 2(h / W)2

Solving and putting 1/W=y, we'll get,

h²/ 2 * y² + GMhy / (R+d)c=GMh / RcL+12(h / L)²

So this follows a quadratic equation ax2+bx+c=0

So that would mean that y would keep decreasing as d increases. Then it would mean that the mass of the photon increases as it rises.