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Chapter 38: Q. 32 (page 1115)

How much energy does it take to ionize a hydrogen atom that is in its first excited state?

Short Answer

Expert verified

The excited hydrogen atom's ionization energy will be 3.4 eV or less.

Step by step solution

01

Given information

The given energy of the first excited state of a hydrogen atom

02

Finding ionization energy of hydrogen

The energy of an electron in a quantum state is calculated as follows:

En=-13.6eVn2

For the first excited state, the quantum number n is given by n=2. Hence the energy of the electron in the first excited state is

E2=-13.6eV22=-3.4eV

The energy of the electron after ionization is

Eion=0

As a result, the energy we must provide is

ΔE=Eion-E2=0-(-3.4eV)=3.4eV

As a result, ionizing a hydrogen atom from its first excited state will require 3.4 eV of energy.

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Most popular questions from this chapter

The wavelengths of light emitted by a firefly span the visible spectrum but have maximum intensity near 550 nm. A typical flash lasts for 100 ms and has a power output of 1.2 mW. How many photons does a firefly emit in one flash if we assume that all light is emitted at the peak intensity wavelength of 550 nm?

An experiment was performed in which neutrons were shot through two slits spaced 0.10 mm apart and detected 3.5 m behind the slits. Figure P38.49 shows the detector output. Notice the 100μmscale on the figure. To one significant figure, what was the speed of the neutrons?

Imagine that the horizontal box of Figure 38.14 is instead oriented vertically. Also imagine the box to be on a neutron star where the gravitational field is so strong that the particle in the box slows significantly, nearly stopping, before it hits the top of the box. Make a qualitative sketch of the n = 3 de Broglie standing wave of a particle in this box.

A proton emits a gamma-ray photon with energy 2.0 MeV in a quantum jump from n =2 to n= 1.

The electron interference pattern of Figure 38.12 was made by shooting electrons with 50keVof kinetic energy through two slits spaced role="math" localid="1650737433408" 1.0μmapart. The fringes were recorded on a detector 1.0mbehind the slits.

a. What was the speed of the electrons? (The speed is large enough to justify using relativity, but for simplicity do this as a nonrelativistic calculation.)

b. Figure 38.12 is greatly magnified. What was the actual spacing on the detector between adjacent bright fringes?
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