Emission and Absorption Spectra AP Physics 2 MCQ – Exam Style Questions etc.
Emission and Absorption Spectra AP Physics 2 MCQ
Unit 15: Modern Physics
Weightage : 15–18%
Exam Style Practice Questions ,Emission and Absorption Spectra AP Physics 2 MCQ
Question
A continuous white-light spectrum illuminates an imaginary monatomic gas with a ground state of -5.0 eV. An optical analyzer reports that wavelengths of 405 nm and 546 nm are absorbed by the gas.
(a) Determine the energies of the photons of light absorbed by the gas.
(b) Show all the excited energy states for the gas atoms in the energy-level diagram above right.
(c) On the energy-level diagram, indicate all possible electron transitions that would produce bright lines in an emission spectrum by drawing arrows showing the transitions.
(d) What is the wavelength of the lowest energy photon possibly produced by an electron relaxing from a higher level energy state to a lower level energy state?
(e) What type of radiation does this wavelength represent?
Answer/Explanation
Ans:
(a) \(E = \frac{hc}{λ} =\frac{ 1240eV • nm}{405nm} = 3.06eV\)
\(E = \frac{hc}{λ} =\frac{ 1240eV • nm}{546nm} = 2.27eV\)
(b) see diagram 
(c) see diagram
(d) \(E_{photon} = E_i − E_f =−1.94eV −(−2.73eV) = 0.79eV\)
\(E = \frac{hc}{λ} →λ =\frac{ hc}{E} =\frac{ 1240eV • nm }{0.79eV} =1570nm\)
(e) Infrared
Question: (12 points, suggested time 25 minutes)
A student is given a glass block that has been specially treated so that the path of light can be seen as the light travels through the glass. The student is asked to design an experiment to measure the index of refraction of the glass. The light source available in the laboratory is a hydrogen lamp that emits red light of a known wavelength.
(a) A linear graph is to be used to determine the index of refraction of the glass. Indicate the quantities that should be graphed and describe how the graph could be used to determine the index of refraction of the glass.
(b) Outline an experimental procedure that could gather the necessary data. Include sufficient detail so that another student could follow your procedure. In addition to the glass block and the hydrogen lamp, the equipment in a typical classroom laboratory is available.
(c) Predict how the path of the light will change as it enters the glass. Support your prediction using a qualitative comparison of the speed of light in glass and the speed of light in air.
(d) Describe the process(es) by which red light from the lamp is produced by hydrogen atoms that are initially in the ground state. Draw and label an energy level diagram that supports the atomic process(es) you describe.
Answer/Explanation
Ans:
n1Sinθ1 = n2Sinθ2 n1 drops out as it is equal to 1 in air.
Sinθ1 = n2Sinθ2 n2 should be solved for as it is the unknown.
\(n_{2} = \frac{Sin\theta _{1}}{Sin\theta _{2}}\) Thus Sinθ1 should be graphed on the y-axis and Sinθ2 should be graphed on the x-axis, so that n2 is equal to \(\frac{y}{x}\) on the slope of the graph.
(b)
The lamp should be set up using a slip so that only a thin beam of light is emitted. The glass block should be in line with this beam and placed on a turnable surface independent of the rest of the apparatus. Measurements can then be made by using a protractor to measure the angle the beam of light makes with the glass block just before entering, and the angle the beam of light makes with the glass block just after entering. All angles should be measured from the normal line. The first angle measured, or the N incident angle N, should be changed so that multiple measurements can be taken.
(c)
The path of the light will bend toward the normal line so that the angle of refraction is less than the angle of incidence. Looking at n1Sinθ1 = n2Sinθ2 we can see that when the index of refraction, n2, is greater than n1 then Sinθ2 must be less than Sinθ1 . Thus θ2< θ1 . The speed of light as it travels through glass is less than the speed of light as it travels through air. Therefore, since \(n = \frac{C}{V}\), when V is less n must increase. Thus nglass is greater than nair.
(d)
Hydrogen atoms in the ground state are excited by other photons. The atoms move to higher energy states as a result of being excited and gaining energy from the photons. The atoms then drop to lower energy states or the ground state and release some or all of the energy they absorbed, respectively.
In step 1 energy is absorbed by the atom and it is excited to a higher energy level. In step 2 the energy is released in the form of a photon.
The atom could have also been excited of n=3 and then dropped to eithter n=2 or n=1. If it dropped to n=2 and then for n=1 the atom would release a photon for times – once for each energy level change