Chapter 41: Q. 29 (page 1207)

A hydrogen atom in its fourth excited state emits a photon with a wavelength of $1282$ nm. What is the atom鈥檚 maximum possible orbital angular momentum (as a multiple of $h$ ) after the emission?

Short Answer

Expert verified

Maximum possible orbital angular momentum is $\frac{3 h}{2 蟺}$ .

Step by step solution

: Given information

Fourth excited state means $n = 5$

Wavelength, $位 = 1282 n m = 1282 脳 10^{- 9} m$

: Simplification

Using Formula , $\frac{1}{位} = R z^{2} (\frac{1}{x^{2}} - \frac{1}{n^{2}})$ , where $位$ is the wavelength , $R$ is rydberg constant , $x$ is the final orbital of electron , $n$ is the initial orbital of electron , $z$ is atomic no

Now for hydrogen $z = 1$

Now , Putting all the values in the formula we get $\frac{1}{1282 脳 10^{- 9}} = 1.01 脳 10^{7} (\frac{1}{x^{2}} - \frac{1}{5^{2}})$

Solving it we get $x = 3$

It means $n = 5 鈬� n = 3$ transition

Now , we know that orbital angular momentum is $\frac{n h}{2 蟺}$

Now after emmision we have $n = 3$

So, the maximum angular momentum comes out to be $\frac{3 h}{2 蟺}$

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 91影视!

One App. One Place for Learning.

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

Get started for free

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

A hydrogen atom in its fourth excited state emits a photon with a wavelength of $1282$ nm. What is the atom鈥檚 maximum possible orbital angular momentum (as a multiple of $h$ ) after the emission?

Short Answer

Step by step solution

: Given information

: Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fluids

Atoms and Radioactivity

Torque and Rotational Motion

Conservation of Energy and Momentum

Force

Translational Dynamics

Study anywhere. Anytime. Across all devices.

91影视

A hydrogen atom in its fourth excited state emits a photon with a wavelength of 1282nm. What is the atom鈥檚 maximum possible orbital angular momentum (as a multiple of h) after the emission?

Short Answer

Step by step solution

: Given information

: Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fluids

Atoms and Radioactivity

Torque and Rotational Motion

Conservation of Energy and Momentum

Force

Translational Dynamics

Study anywhere. Anytime. Across all devices.

A hydrogen atom in its fourth excited state emits a photon with a wavelength of $1282$ nm. What is the atom鈥檚 maximum possible orbital angular momentum (as a multiple of $h$ ) after the emission?