Ch.6 - Electronic Structure of Atoms

Problem 35

Chapter 6, Problem 35

Does the hydrogen atom 'expand' or 'contract' when an electron is excited from the n = 1 state to the n = 3 state?

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Understand the concept of electron orbitals in a hydrogen atom. The principal quantum number, 'n', indicates the size and energy of the orbital where the electron resides.

Recognize that as the principal quantum number 'n' increases, the electron moves to a higher energy level, which is further away from the nucleus.

Relate the distance of the electron from the nucleus to the size of the electron cloud or orbital. A higher 'n' value means a larger orbital.

Conclude that when an electron is excited from a lower energy level (n = 1) to a higher energy level (n = 3), it moves to an orbital that is further from the nucleus.

Determine that the hydrogen atom 'expands' because the electron occupies a larger orbital when it is excited from the n = 1 state to the n = 3 state.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Quantum States

Quantum states refer to the specific energy levels that electrons occupy in an atom. Each state is characterized by a principal quantum number (n), which indicates the energy level and distance from the nucleus. For hydrogen, the n = 1 state is the ground state, while n = 3 is an excited state, where the electron is further from the nucleus and has higher energy.

Electron Excitation

Electron excitation occurs when an electron absorbs energy and transitions from a lower energy level to a higher one. In the case of hydrogen, moving from n = 1 to n = 3 means the electron gains energy, which can be provided by various sources such as heat or light. This process results in the electron being in a less stable, higher energy state.

Atomic Radius

The atomic radius is a measure of the size of an atom, typically defined as the distance from the nucleus to the outermost electron shell. When an electron is excited to a higher energy level, such as from n = 1 to n = 3, the average distance of the electron from the nucleus increases, effectively causing the atom to 'expand' in size due to the electron's higher energy state.

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Textbook Question

Molybdenum metal must absorb radiation with an energy higher than 7.22 * 10-19 J ('energy threshold') before it can eject an electron from its surface via the photoelectric effect. (b) What wavelength of radiation will provide a photon of this energy?

Molybdenum metal must absorb radiation with an energy higher than 7.22 * 10-19 J ('energy threshold') before it can eject an electron from its surface via the photoelectric effect. (c) If molybdenum is irradiated with light of wavelength of 240 nm, what is the maximum possible velocity of the emitted electrons?

Titanium metal requires light with a maximum wavelength of 286 nm to emit electrons. (a) What is the minimum energy of the photons necessary to emit electrons from titanium via the photoelectric effect? (b) If titanium is irradiated with light of wavelength 276 nm, what is the maximum possible kinetic energy of the emitted electrons?

Textbook Question

Classify each of the following statements as either true or false: (a) A hydrogen atom in the n = 3 state can emit light at only two specific wavelengths (b) a hydrogen atom in the n = 2 state is at a lower energy than one in the n = 1 state (c) the energy of an emitted photon equals the energy difference of the two states involved in the emission.

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Textbook Question

Is energy emitted or absorbed when the following electronic transitions occur in hydrogen? (a) from n = 3 to n = 2 (c) an electron adds to the H⁺ ion and ends up in the n = 2 shell?

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Textbook Question

Is energy emitted or absorbed when the following electronic transitions occur in hydrogen? (b) from an orbit of radius 0.846 nm to one of radius 0.212 nm

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