Energy & Telescopic Physics/Astronomy



NOTE: I am only posting in this forum because nobody will answer my question in the Homework forum. Please do not move this.

I am having some difficulties with my latest assignment. I would greatly appreciate it if someone could answer the questions:

1.) Figure 2.23 on page 66 of your textbook shows the wavelengths of the first three Balmer lines: Hα, Hβ, and Hγ. Given your result in part a), what is the energy difference between the ground state and the first four excited states of a hydrogen atom?

Firstly, Figure 2.23 on page 66 has two versions of the Balmer lines of hydrogen, so which one are we supposed to use?
I would assume that we need to use the one at 320 m/s instead of 0 m/s, so that we have a value for speed when we try to find the frequency of the hydrogen.
Also, what exactly do Hα, Hβ, and Hγ represent? Are they the different excited states of the hydrogen atom?
How are we expected to compare the energy difference between the ground state and the first four excited states of a hydrogen atom? What are they represented by in the question?

2.) Popular culture often describes Mars as being inhabited by "little green men". Imagine there is a green (500 nm light), 50 cm tall Martian standing on the surface of Mars. How big a telescope would you need to observe the Martian from the Earth if your obesrvation was diffraction limited? You may assume that the Sun, Earth, and Mars are lined up when the observation is made.

I think that I have the right method of solving this problem. However, we are given a lot of space for our answer, and my answer is much shorter than all that space. On the last assignment, we were given a lot of space for question 3, and we were expected to use it all. So I'm assuming the case is the same for this assignment.

This is what I did: (Tell me if there are any errors, or anything I missed that was supposed to be taken into account).

distance = semi-major axis of Mars - semi-major axis of Earth
d = Am - Ae = 7.83 x 1010 m
λ = 500 nm = 0.5 μm
h = 0.5 m

angular resolution = height / distance = 0.5 / 7.83 x 10^10 =
angular resolution = 6.386 x 10^-12 rad

diameter = 0.25 x wavelength / angular resolution = (0.25)(0.5) / (6.386 x 10^-12)
diameter = 1.957 x 10^10 μm

Therefore, the diameter of the telescope is approximately 20,000 m.
However, this answer does not seem like enough for the amount of space we are given.

Thank you for any help you can provide.


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