Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

What is the third-longest wavelength in the absorption spectrum of hydrogen?

Short Answer

Expert verified

The wavelength of the third longest wave is 97.3 nm

Step by step solution

01

Given information

The absorption line for hydrogen gas containing atoms in the ground state has the longest wavelength of 121.6nm.

02

Calculations

Our goal is to discover the hydrogen atom's absorption spectrum's third longest wavelength.

Assume we have a quantized system, such as the hydrogen atom, which has discrete energy levels rather than a continuum. When an electron absorbs a photon of a specific energy, it makes a quantum jump from a lower energy level Eito a higher energy level Ej. The amount of energy required to excite an electron from its ithto its jthstate is,

Eij=ΔEij=EjEiwhereEj>Ei=hcλijλij=hcEjEi(1)

Eijdenotes that the quantized system excites from the Eistate to the Ejstate by absorbing an amount of energy equal to role="math" localid="1650736975140" Eij. We may deduce from (1) that λijis inversely proportional to ΔEij, and since ΔE21<ΔE31<ΔE41λ12>λ13>λ14

As a result, the third longest wavelength is λ14. The energy of a particular state n for the hydrogen atom where Z=1 is calculated using Eq. (38.38).

En=13.6eVn22

We get by swapping (2) for (1),

λij=hc13.6eVj2+13.6eVi2wherej>iλ14=4.1357×1015eV.s×3×108m.s113.6eV42+13.6eV12=9.73×108m=97.3nm

The wavelength of the third longest wave is 97.3 nm

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.

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

In the atom interferometer experiment shown in Figure 38.13laser cooling techniques were used to cool a dilute vapor of sodium atoms to a temperature of 0.0010K=1.0mK. The ultracold atoms passed through a series of collimating apertures to form the atomic beam you see circling the figure from the left. The standing light waves were created from a laser beam with a wavelength of 590nm.

a. What is the rms speed vmeof a sodium atom (A-23)in a gas at this temperature 1.0mK?

b. By treating the laser beam as if it were a diffraction grating. cakculate the first-order diffraction angle of a sodium atom traveling with the rms speed of part a.

c. allow far apart are points Band Cif the second sanding wave is 10cmfrom the first?

d. Because interference is observed between the two paths, each individual atom is apparently present at both point Band point C. Describe, in your own words, what this experiment tells you about the nature of matter.

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.

The charge on a muon-a subatomic particle is -e and its mass 207 times that of an electron-

which is confined in a 15-pm-long, one-dimensional box.

(1 pm = 1 picometer = 10-12 m.)

What is the wavelength, in nm, of the photon emitted in a quantum jump from n=2 to n=1

The cosmic microwave background radiation is light left over from the Big Bang that has been Doppler-shifted to microwave frequencies by the expansion of the universe. It now fills the universe with 450 photons/cm3 at an average frequency of 160 GHz. How much energy from the cosmic microwave background, in MeV, fills a small apartment that has 95 m2 of floor space and 2.5-m-high ceilings?

What is the length of a one-dimensional box in which an electron in the n=1state has the same energy as a photon with a wavelength of 600nm?

See all solutions

Recommended explanations on Physics Textbooks

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