Question 7
7
9 marks
Question 7(a)
7(a)
The emission spectrum of atomic hydrogen consists of a number of discrete wavelengths. Explain how this observation leads to an understanding that there are discrete electron energy levels in atoms.
Mediumstructured2 marks
Answer
each wavelength is associated with a discrete change in energy M1 discrete energy change / difference implies discrete levels A1 [2]
Question 7(b)
7(b)
Some electron energy levels in atomic hydrogen are illustrated in Fig. 7.1. The longest wavelength produced as a result of electron transitions between two of the energy levels shown in Fig. 7.1 is \(4.0 \times 10^{-6} \mathrm{~m}\).
structured5 marks
Question 7(b)(i)
7(b)(i)
On Fig. 7.1, 1. draw, and mark with the letter L , the transition giving rise to the wavelength of \(4.0 \times 10^{-6} \mathrm{~m}\), 2. draw, and mark with the letter S , the transition giving rise to the shortest wavelength.
Mediumstructured2 marks
Answer
1. arrow from -0.54 eV to -0.85 eV , labelled \(\mathrm{L} \quad\) B1 [1] 2. arrow from -0.54 eV to -3.4 eV , labelled S B1 [1] (two correct arrows, but only one label - allow 2 marks) (two correct arrows, but no labels - allow 1 mark)
Question 7(b)(ii)
7(b)(ii)
Calculate the wavelength for the transition you have shown in (i) part 2. m
Mediumstructured3 marks
Answer
\(E=h c / \lambda\) C1 \((3.4-0.54) \times 1.6 \times 10^{-19}=\left(6.63 \times 10^{-34} \times 3.0 \times 10^{8}\right) / \lambda \quad\) C1 \(\lambda=4.35 \times 10^{-7} \mathrm{~m} \quad\) A1
Question 7(c)
7(c)
Photon energies in the visible spectrum vary between approximately 3.66 eV and 1.83 eV . Determine the energies, in eV, of photons in the visible spectrum that are produced by transitions between the energy levels shown in Fig. 7.1. photon energies eV
Mediumstructured2 marks
Answer
\(-1.50 \rightarrow-3.4=1.9 \mathrm{eV}\) \(-0.85 \rightarrow-3.4=2.55 \mathrm{eV}\) (allow 2.6 eV ) \(-0.54 \rightarrow-3.4=2.86 \mathrm{eV}\) (allow 2.9 eV ) 3 correct, 2 marks with -1 mark for each additional energy 2 correct, 1 mark but no marks if any additional energy differences B2
Question 8
8
White light is incident on a cloud of cool hydrogen gas, as illustrated in Fig. 8.1. The spectrum of the light emerging from the gas cloud is found to contain a number of dark lines.
structured4 marks
Question 8(a)
8(a)
Explain why these dark lines occur.
Mediumstructured3 marks
Answer
photon 'absorbed' by electron B1 photon has energy equal to difference in energy of two energy levels B1 electron de-excites emitting photon (of same energy) in any direction B1 [3]
Question 8(b)
8(b)
Some electron energy levels in a hydrogen atom are illustrated in Fig. 8.2. One dark line is observed at a wavelength of 435 nm .
structured1 marks
Question 8(b)(ii)
8(b)(ii)
On Fig. 8.2, draw an arrow to indicate the energy change that gives rise to this dark line.
Mediumstructured1 marks
Answer
arrow pointing in either direction between -3.41 eV and \(-0.55 \mathrm{eV} \quad\) B1 [1]
Question 7
7
11 marks
Question 7(a)
7(a)
Explain how the line spectrum of hydrogen provides evidence for the existence of discrete electron energy levels in atoms.
Mediumstructured3 marks
Answer
each line represents photon of specific energy
Question 7(b)
7(b)
Some electron energy levels in atomic hydrogen are illustrated in Fig. 7.1. Two possible electron transitions A and B giving rise to an emission spectrum are shown. These electron transitions cause light of wavelengths 654 nm and 488 nm to be emitted.
structured4 marks
Question 7(b)(i)
7(b)(i)
On Fig. 7.1, draw an arrow to show a third possible transition.
Mediumstructured1 marks
Answer
arrow from -0.85 eV level to -1.5 eV level
Question 7(b)(ii)
7(b)(ii)
Calculate the wavelength of the emitted light for the transition in (i). wavelength = m
Mediumstructured3 marks
Answer
\(\Delta E=h c / \lambda\) photon emitted as a result of energy change of electron specific energy changes so discrete levels
Question 7(c)
7(c)
The light in a beam has a continuous spectrum of wavelengths from 400 nm to 700 nm . The light is incident on some cool hydrogen gas, as illustrated in Fig. 7.2. Using the values of wavelength in (b), state and explain the appearance of the spectrum of the emergent light.
Mediumstructured4 marks
Question 7
7
7 marks
Question 7(a)
7(a)
A beam of white light passes through a cloud of cool gas. The spectrum of the transmitted light is viewed and contains a number of dark lines. Explain why these dark lines occur.
Mediumstructured4 marks
Answer
photon absorbed (by electron) and electron excited B1 photon energy equal to difference in (energy of two) energy levels B1 photon energy relates to a single wavelength / single frequency B1 electron de-excites and emits photon in any direction B1
Question 7(b)
7(b)
Some energy levels for the electron in an isolated hydrogen atom are illustrated in Fig. 7.1. Table 7.1 shows the wavelengths of photons that are emitted in the transitions to n=2 from the other energy levels shown in Fig. 7.1. The energy associated with the energy level n=2 is -3.40 eV . Calculate the energy, in J , of energy level n=3. energy = ..... J
Mediumstructured3 marks
Answer
\(\frac{h c}{\lambda}=\Delta E\) C1 uses 658 nm C1 \[ \begin{aligned} \frac{6.63 \times 10^{-34} \times 3.00 \times 10^{8}}{658 \times 10^{-9}}=-\mathrm{E}_{1}-\left(-3.40 \times 1.60 \times 10^{-19}\right) E_{1}=-2.42 \times 10^{-19} \mathrm{~J} \end{aligned} \] A1
Question 8
8
Fig. 8.1 shows the lowest four energy levels of an electron in an isolated atom. Fig. 8.2 shows the lines in the emission spectrum of the atom that correspond to the transitions of the electron from n=3 to n=1 and from n=4 to n=1.
structured6 marks
Question 8(a)
8(a)
Explain, with reference to photons, why there is a single frequency of electromagnetic radiation that corresponds to each of these transitions.
Mediumstructured2 marks
Answer
transition (emits) (one) photon with energy equal to the difference in energy between the two levels B1 frequency of radiation corresponds to energy of photon B1
Question 8(b)
8(b)
4 marks
Question 8(b)(i)
8(b)(i)
On Fig. 8.2, draw a line that corresponds to the transition of the electron from n=2 to n=1. Label this line A.
Easystructured2 marks
Answer
line to the left of the pair in Fig. 8.2, labelled A B1 larger gap between line A and the nearest of the pair in Fig. 8.2 than between the lines in the pair B1
Question 8(b)(ii)
8(b)(ii)
On Fig. 8.2, draw a line that corresponds to the transition of the electron from n=3 to n=2. Label this line B.
Easystructured2 marks
Answer
line to the left of both the pair in Fig. 8.2 and line A, labelled B B1 larger gap between line B and line A than between line A and the nearest one of the pair in Fig. 8.2 B1
Question 8(c)
8(c)
The frequency of radiation represented by line A is \(f_{\mathrm{A}}\). The frequency of radiation represented by line B is \(f_{\mathrm{B}}\). The energy of the ground state (n=1) is \(E_{1}\). Determine an expression, in terms of \(f_{\mathrm{A}}, f_{\mathrm{B}}, E_{1}\) and the Planck constant h, for the energy \(E_{3}\) of the energy level n=3.
Hardstructured0 marks
Answer
E=h f C1 \(E_{3}=E_{1}+h\left(f_{\mathrm{A}}+f_{\mathrm{B}}\right)\) A1