Chapter 41: Q. 17 (page 1207)

An electron accelerates through a $12.5 V$ potential difference, starting from rest, and then collides with a hydrogen atom, exciting the atom to the highest energy level allowed. List all the possible quantum-jump transitions by which the excited atom could emit a photon and the wavelength (in nm) of each.

Short Answer

Expert verified

The wavelength is $λ_{1} = 656.08 n m$ , $λ_{2} = 102.56 n m$ and $λ_{3} = 121.56 n m$ .

Step by step solution

Given Information

We need to find the emit a photon and the wavelength.

Simplify

The atom could emit a photon in the $3$ possible quantum-jump transition:

role="math" localid="1650276055698" $3 \to 2, 3 \to 1 a n d 2 \to 1$

Now, for $3 \to 2$ :

$E_{1} = - 1.51 e V - (- 3.40 e V) E_{1} = - 1.51 e V + 3.40 e V E_{1} = 1.89 e V$

for $3 \to 1$ :

$E_{2} = - 1.51 e V - (- 13.60 e V) E_{2} = - 1.51 e V + 13.60 e V E_{2} = 12.09 e V$

for

2 \to 1

$E_{3} = - 3.40 e V - (- 13.60 e V) E_{3} = - 3.40 e V + 13.60 e V E_{3} = 10.2 e V$

Calculation

Now, finding the wavelength :

$λ_{1} = \frac{h c}{E_{1}} λ_{1} = \frac{12.40 e V \times n m}{1.89 e V} λ_{1} = 656.08 n m λ_{2} = \frac{h c}{E_{2}} λ_{2} = \frac{12.40 e V \times n m}{12.09 e V} λ_{2} = 102.56 n m λ_{3} = \frac{h c}{E_{3}} λ_{3} = \frac{12.40 e V \times n m}{10.2 e V} λ_{3} = 121.56 n m$

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!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Short Answer

Step by step solution

Given Information

Simplify

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Energy Physics

Geometrical and Physical Optics

Electric Charge Field and Potential

Electricity and Magnetism

Torque and Rotational Motion

Physical Quantities And Units

Study anywhere. Anytime. Across all devices.