A rocket is fired from the earth to the moon at a speed of 0.990c. Let two events be 'rocket leaves earth' and 'rocket hits moon.' In the earth's reference frame, calculate ∆x, ∆t, and the spacetime interval s for these events.
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35. Special Relativity
Inertial Reference Frames
Problem 10a
Textbook Question
Identify the element for each of these electron configurations. Then determine whether this configuration is the ground state or an excited state. 1s² 2s² 2p⁵

1
Step 1: Analyze the given electron configuration: 1s² 2s² 2p⁵. This configuration represents the distribution of electrons in the atomic orbitals of an atom. The numbers (1, 2) indicate the energy levels, the letters (s, p) indicate the type of orbital, and the superscripts (², ⁵) indicate the number of electrons in each orbital.
Step 2: Count the total number of electrons in the configuration. Add the superscripts: 2 (from 1s²) + 2 (from 2s²) + 5 (from 2p⁵) = 9 electrons. This tells us the atom has 9 electrons, which corresponds to the atomic number of the element.
Step 3: Use the periodic table to identify the element with an atomic number of 9. The element with 9 protons (and thus 9 electrons in a neutral atom) is fluorine (F).
Step 4: Determine whether the configuration is in the ground state or an excited state. The given configuration (1s² 2s² 2p⁵) follows the Aufbau principle, Hund's rule, and the Pauli exclusion principle, which means it is the most stable arrangement of electrons for fluorine. Therefore, this is the ground state configuration.
Step 5: Conclude that the element is fluorine (F), and the configuration 1s² 2s² 2p⁵ represents its ground state.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Electron Configuration
Electron configuration describes the distribution of electrons in an atom's orbitals. It is represented by a series of numbers and letters indicating the energy levels and types of orbitals occupied by electrons. For example, in the configuration 1s² 2s² 2p⁵, the numbers indicate the principal energy levels, while 's' and 'p' denote the types of orbitals.
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Ground State vs. Excited State
The ground state of an atom is its lowest energy configuration, where electrons occupy the lowest available energy levels. An excited state occurs when one or more electrons have absorbed energy and moved to higher energy levels than those in the ground state. Identifying whether an electron configuration represents a ground or excited state is crucial for understanding the atom's energy state.
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Periodic Table and Element Identification
The periodic table organizes elements based on their atomic number and electron configurations. Each element has a unique electron configuration that determines its chemical properties. By analyzing the given configuration 1s² 2s² 2p⁵, one can identify the element as fluorine, which has an atomic number of 9, and determine its state based on the arrangement of its electrons.
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