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’s maximum possible orbital angular momentum (as a multiple of $h$ ) after the emission?

Short Answer

Expert verified

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

Step by step solution

: Given information

Fourth excited state means $n = 5$

Wavelength, $λ = 1282 n m = 1282 \times 10^{- 9} m$

: Simplification

Using Formula , $\frac{1}{λ} = R z^{2} (\frac{1}{x^{2}} - \frac{1}{n^{2}})$ , where $λ$ 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 $\frac{1}{1282 \times 10^{- 9}} = 1.01 \times 10^{7} (\frac{1}{x^{2}} - \frac{1}{5^{2}})$

Solving it we get $x = 3$

It means $n = 5 \Rightarrow n = 3$ transition

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

Now after emmision we have $n = 3$

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

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

Short Answer

Step by step solution

: Given information

: Simplification

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A hydrogen atom in its fourth excited state emits a photon with a wavelength of 1282nm. What is the atom’s 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

Kinematics Physics

Nuclear Physics

Geometrical and Physical Optics

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Thermodynamics

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’s maximum possible orbital angular momentum (as a multiple of $h$ ) after the emission?