Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Problem 37

Is energy emitted or absorbed when the following electronic transitions occur in hydrogen? (a) from \(n=3\) to \(n=2\), (b) from an orbit of radius \(0.846 \mathrm{nm}\) to one of radius 0.212 \(\mathrm{nm},(\mathbf{c})\) an electron adds to the \(\mathrm{H}^{+}\) ion and ends up in the \(n=2\) shell?

Short Answer

Expert verified
In all the given transitions, energy is emitted. For transition (a) from \(n=3\) to \(n=2\), energy is emitted as the electron moves to a lower energy level. For transition (b) from an orbit of radius 0.846nm to one of radius 0.212nm, energy is emitted due to a move from a higher to lower energy level. Lastly, for transition (c) when an electron adds to the \(\mathrm{H}^{+}\) ion and ends up in the \(n=2\) shell, energy is emitted as the system moves from an ionic state to an atomic state.

Step by step solution

01

Analyze the transition (a) from \(n=3\) to \(n=2\)

The electron is transitioning from a higher energy level (\(n=3\)) to a lower energy level (\(n=2\)). According to the Bohr's atomic model, when an electron comes down to a smaller shell, energy is emitted. So, in this transition, energy is emitted.
02

Analyze the transition (b) from an orbit of radius 0.846nm to one of radius 0.212nm

Here, it is not directly given which energy level the electron is transitioning from or to. However, we know that according to Bohr's model, radius of the \(n^{th}\) orbit, \(r_n\) is directly proportional to \(n^2\) (i.e. \(r_n \propto n^2\)). Therefore, a transition from a larger orbit (i.e larger \(n\)) to a smaller orbit corresponds to a transition from a higher energy level to a lower energy level. Therefore, in this transition, similar to the previous one, energy is emitted.
03

Analyze the transition (c) an electron adds to the \(\mathrm{H}^{+}\) ion and ends up in the \(n=2\) shell?

When an electron is added to a \(\mathrm{H}^{+}\) ion, it changes from the ionic state to the atomic state. This transition corresponds to a decrease in energy level (from ionization level to \(n=2\)), and thus, energy will be emitted in this case too. Therefore, for all the given transitions, energy is emitted. Please note that the actual amount of energy emitted or absorbed in such transitions can be calculated using the formula for the energy differences in the Bohr's atomic model, but since this exercise only asks for whether energy is emitted or absorbed, specific calculations are not required.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

(a) The average distance from the nucleus of a 3 s electron in a chlorine atom is smaller than that for a \(3 p\) electron. In light of this fact, which orbital is higher in energy? (b) Would you expect it to require more or less energy to remove a 3 s electron from the chlorine atom, as compared with a $2 p$ electron?

The speed of sound in dry air at \(20^{\circ} \mathrm{C}\) is $343 \mathrm{~m} / \mathrm{s}$ and the lowest frequency sound wave that the human ear can detect is approximately \(20 \mathrm{~Hz}\) (a) What is the wavelength of such a sound wave? (b) What would be the frequency of electromagnetic radiation with the same wavelength? (c) What type of electromagnetic radiation would that correspond to? [Section 6.1]

Sketch the shape and orientation of the following types of orbitals: \((\mathbf{a}) s,(\mathbf{b}) p_{z},(\mathbf{c}) d_{x y}\).

Identify the specific element that corresponds to each of the following electron configurations and indicate the number of unpaired electrons for each: (a) \(1 s^{2} 2 s^{2}\), (b) \(1 s^{2} 2 s^{2} 2 p^{4}\) (d) \([\mathrm{Kr}] 5 s^{2} 4 d^{10} 5 p^{4}\) (c) \([\mathrm{Ar}] 4 s^{1} 3 d^{5}\)

If human height were quantized in 1 -cm increments, what would happen to the height of a child as she grows up: (i) the child's height would never change, (ii) the child's height would continuously increase, (iii) the child's height would increase in jumps of \(6 \mathrm{~cm}\), or (iv) the child's height would increase in "jumps" of \(1 \mathrm{~cm}\) at a time?
See all solutions

Recommended explanations on Chemistry Textbooks

Inorganic Chemistry

Read Explanation

Nuclear Chemistry

Read Explanation

Kinetics

Read Explanation

Physical Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Chemical Analysis

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free