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** Missing info: Lines per mm = 500 **
Ans: The wavelength is = λ = 1414.21 nm
Explanation:
The formula for diffraction grading is:
dsinθ = mλ --- (1)
Where
d = 1/lines-per-meter = (1/500)*10^-3 = 2 * 10^-6
m = order = 1
λ = wavelength
θ = 45°
Plug in the values in (1):
(1) => 2*10^-6*sin(45°) = (1)λ
=> λ = 1414.21 nm
Answer:
System D --> System C --> System A --> System B
Explanation:
The gravitational force between two masses m1, m2 separated by a distance r is given by:

where G is the gravitational constant. Let's apply this formula to each case now to calculate the relative force for each system:
System A has masses m and m separated by a distance r:

system B has masses m and 2m separated by a distance 2r:

system C has masses 2m and 3m separated by a distance 2r:

system D has masses 4m and 5m separated by a distance 3r:

Now, by looking at the 4 different forces, we can rank them from the greatest to the smallest force, and we find:
System D --> System C --> System A --> System B
The frequency of the wave will not change