A) 750 m
First of all, let's find the wavelength of the microwave. We have
is the frequency
is the speed of light
So the wavelength of the beam is

Now we can use the formula of the single-slit diffraction to find the radius of aperture of the beam:

where
m = 1 since we are interested only in the central fringe
D = 30 km = 30,000 m
a = 2.0 m is the aperture of the antenna (which corresponds to the width of the slit)
Substituting, we find

and so, the diameter is

B) 0.23 W/m^2
First we calculate the area of the surface of the microwave at a distance of 30 km. Since the diameter of the circle is 750 m, the radius is

So the area is

And since the power is

The average intensity is

This is an interesting (read tricky!) variation of Rydberg Eqn calculation.
Rydberg Eqn: 1/λ = R [1/n1^2 - 1/n2^2]
Where λ is the wavelength of the light; 1282.17 nm = 1282.17×10^-9 m
R is the Rydberg constant: R = 1.09737×10^7 m-1
n2 = 5 (emission)
Hence 1/(1282.17 ×10^-9) = 1.09737× 10^7 [1/n1^2 – 1/25^2]
Some rearranging and collecting up terms:
1 = (1282.17 ×10^-9) (1.09737× 10^7)[1/n2 -1/25]
1= 14.07[1/n^2 – 1/25]
1 =14.07/n^2 – (14.07/25)
14.07n^2 = 1 + 0.5628
n = √(14.07/1.5628) = 3
Answer:
I. 6 cells .
II. Series connection.
Explanation:
I. Determination of the number of cells needed.
From the question given above,
Total voltage (V) = 9 V
1.5 V = 1 cell
Number of cells needed =?
The number of cells needed to make the 9V battery can be obtained as follow:
1.5 V = 1 cell
Therefore,
9 V = 9 V × 1 cell / 1.5 V
9 V = 6 cells
Thus, 6 cells of 1.5 V each is needed
II. Determination of the connection line
Total voltage (Vₜ) = 9 V
Cell 1 (V₁) = 1.5 V
Cell 2 (V₂) = 1.5 V
Cell 3 (V₃) = 1.5 V
Cell 4 (V₄) = 1.5 V
Cell 5 (V₅) = 1.5 V
Cell 6(V₆ ) = 1.5 V
For parrall connection:
Vₜ = V₁ = V₂ = V₃ = V₄ = V₅ = V₆
9 V = 1.5 V =... = 1.5 V
For series connection:
Vₜ = V₁ + V₂ + V₃ + V₄ + V₅ + V₆
9 = 1.5 + 1.5 + 1.5 + 1.5 + 1.5 + 1.5
9 V = 9 V
From the illustration above, we can see that series connection of each cells will give a total volt of 9 V unlike the parallel connection which resulted to 1.5 V.
Therfore, the cells should be arranged in series connection
I believe it is D I’m sorry if it’s wrong