Figure below depicts three hypothetical atoms. Energy levels are represented as horizontal segments. The distance between the segments is representative of the energy difference between the various levels. All possible transitions between energy levels are indicated by arrows.

Scientists can observe the spectral lines of atoms that are dominant in far-away galaxies. Due to the speed at which these galaxies are travelling, these lines are shifted, but their pattern remains the same. This allows researchers to use the spectral pattern to determine which atoms they are seeing. Table - 1 below shows spectroscopic measurements made by researchers trying to determine the atomic makeup of a particular far-away galaxy. Light energy is not measured directly, but rather is determined from measuring the frequency of light, which is proportional to the energy.
Table – 1
Frequencies Measured |
868440 |
880570 |
879910 |
856390 |
(i) For each of three hypothetical atoms (Atom 1, Atom 2 and Atom 3), Figure depicts the –
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Ans.
(i)
Sol. According to the passage, when an electron moves from one possible energy state to another, the atom emits light whose energy level equals the difference in energy levels between the two states. This difference is seen as a spectral line, which is shown by each arrow in Figure.
(ii)
Sol. The frequencies listed in Table 1 indicate measurements of light energy. In the figure, the length of an arrow also indicates an amount of light energy. Thus, if the difference between measurements in Table 1 corresponds to the difference between the lengths of the arrows in one of the three atoms depicted in the figure, this correlation is a strong indication that the scientists are observing an atom like that hypothetical one. In Table 1, the two frequencies 868440, 880570 are high numbers and very close to each other in value compared to the other two frequencies–just as the two longest arrows in the depiction of Atom 3 are very close in length to each other and significantly longer than the other arrows depicted for Atom 3.
(iii)
Sol. To determine the number of forbidden transitions in any one of the atoms, start at each energy level (horizontal line) and look for an arrow connecting it to each of the other energy levels. Each pair of levels that don’t connect indicate a forbidden transition. Atom 1 has a total of two forbidden transitions. Atom 2 has only one forbidden transition. Atom 3 has no forbidden transitions
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