Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 38: Problem 56

What is the ionization energy of a hydrogen atom excited to the \(n=2\) state?

Short Answer

Expert verified
Answer: The ionization energy of a hydrogen atom excited to the \(n=2\) state is \(3.4\,\text{eV}\).

Step by step solution

01

Identify the hydrogen atomic energy level equation

The energy levels of a hydrogen atom can be calculated using the following equation: \(E_n = -\frac{13.6\,\text{eV}}{n^2}\) where \(n\) is the principal quantum number, and the energy \(E_n\) is in electron volts (eV).
02

Calculate the energy of the hydrogen atom at the \(n=2\) state

Using the energy level equation, we can calculate the energy of the hydrogen atom at the \(n=2\) state: \(E_2 = -\frac{13.6\,\text{eV}}{2^2} = -\frac{13.6\,\text{eV}}{4} = -3.4\,\text{eV}\)
03

Calculate the energy of the ionized state

When the hydrogen atom is ionized, the electron is completely removed and the energy of the atom is \(0\,\text{eV}\).
04

Calculate the ionization energy

The ionization energy is the difference in energy between the \(n=2\) state and the ionized state: Ionization Energy = \(E_\text{ionized} - E_2 = 0\,\text{eV} - (-3.4\,\text{eV}) = 3.4\,\text{eV}\) So, the ionization energy of a hydrogen atom excited to the \(n=2\) state is \(3.4\,\text{eV}\).

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

An excited hydrogen atom, whose electron is in an \(n=4\) state, is motionless. When the electron falls into the ground state, does it set the atom in motion? If so, with what speed?

Hund's rule, a component of the Aufbauprinzip (construction principle), states that as one moves across the periodic table, with increasing atomic number, the available electron subshells are filled successively with one electron in each orbital, their spins all parallel; only when all orbitals in a subshell contain one electron are second electrons, with spins opposite to the first, placed in the orbitals. Explain why the ground state electron configurations of successive elements should follow this pattern.

An excited hydrogen atom emits a photon with an energy of \(1.133 \mathrm{eV}\). What were the initial and final states of the hydrogen atom before and after emitting the photon?

Transition metals can be defined as elements where the \(d\) shell goes from empty to full. How many transition metals are there in each period? a) 2 b) 6 c) 10 d) 14

You hold in your hands both a green \(543-n m, 5.00-m W\) laser and a red, \(633-\mathrm{nm}, 4.00\) -mW laser. Which one will produce more photons per second, and why?
See all solutions

Recommended explanations on Physics Textbooks

Fluids

Read Explanation

Mechanics and Materials

Read Explanation

Geometrical and Physical Optics

Read Explanation

Solid State Physics

Read Explanation

Quantum Physics

Read Explanation

Classical Mechanics

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