The spectrum of an excited gas is a series of discrete lines because
a. in multielectron atoms, each electron emits a certain, unique wavelength.
b. different atoms in the gas have different ionization states.
c. other wavelengths are absorbed by the gas.
d. electrons exist in quantized energy states, and only certain transitions are possible.
2. a low-pressure gas discharge tube emits
a. a discrete spectrum
b. a continuous spectrum
c. an absorption spectrum
d. a beta spectrum

Answers:

1) d. Electrons exist in quantized energy states, and only certain transitions are possible.

2)  a. a discrete spectrum

First, let's start by explaining that every atom is capable of emitting or absorbing electromagnetic radiation, however, this is only possible at some frequencies that are characteristic of each chemical element.  

In other words:  

Electrons in an atom can only be in a number of allowed energy states. This means that in the fundamental state of the atom, electrons are in their lowest energy states and are "allowed to jump" to a limited number of higher energy levels, and for this the atom must gain a very specific amount of energy (which can be thermal energy). Now, when the opposite happens, that is, that the electron "falls" to a lower state of energy, a very specific amount of energy is released in the form of discrete energy packets, which are the well-known photons.  

Therefore, each spectral line corresponds to a particular transition between energy states of the atoms of a particular element. In the specific case of emission lines, these are formed when the electron falls back to a lower energy level releasing a photon.  

Having this clear, we move on to the following:  

If thermal energy is supplied to a certain element in its gas phase, it will be stimulated and its atoms will emit radiation at certain frequencies (wavelengths) of the visible spectrum, thus forming an emission spectrum showing discrete lines of certain colors.  

Then, in the case of an excited gas and specifically its emission spectrum, it will show discrete (not continuous) lines. This is because when the gas is radiated with white light, the electrons jump from their fundamental state to higher energy levels (excited state) and then fall back to lower energy levels, thus producing the emission of a photon of a defined and specific wavelength, which will appear as a specific line in the emission spectrum of the gas.

As explained in the previous answer, an electron can only emit certain frequencies of light (certain colors) when moving from a high energy level to a lower one. This is because the light behaves like a stream of small energy packets (it is quantized), therefore, the energy levels in the atoms are quantized.

In the case of a tube containing a noble gas inside at low pressure that is subjected to an electric field when placed between two electrodes, the discharge of the gas occurs causing the electrons present in the gas to transition from an energy level to another, releasing photons of specific wavelengths (colors).

Therefore, if a spectroscopy  analasis is done on the emitted light, a discrete spectrum will be observed.

It should be noted that this is the operation principle of the fluorescent and sodium lamps.