Logo
Home Study Material Contact Search
AI Chat FREE
  1. sciences
  2. physics
  3. suppose the electron in a hydrogen atom is modeled

Suppose the electron in a hydrogen atom is modeled as an electron in a one-dimensional box...

Free

50.1K

Verified Solution

Question

Physics

Suppose the electron in a hydrogen atom is modeled as anelectron in a one-dimensional box of length equal to the Bohrdiameter, 2a0. What would be the ground-stateenergy of this \"atom\"?
______________eV

Answer & Explanation Solved by verified expert
4.0 Ratings (761 Votes)

With the following data:

  • Length of the box : L = 2 a o  
  • a o is bohr radius -- 0.0529 nm --   

Allowed energy of a particle in one dimensional box is

               E n = n 2 h 2 / 8 m L 2     

Where   m is mass electron and h is plancks constant

Ground state energy of the atom is:

           E =   h 2 / 8 m L 2    

               = ( 6.635 *10 -34 Js ) 2 / ( 8)(9.11*10-31 kg ) ( 2*0.0529 *10-9 ) 2  

               =  53.963*10-19 J

               = 33.7273 eV

Actual ground state energy of hydrogen atom is: -13.6 eV

Diving:

              33.7273 / 13.6   = 2.4799 times
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Algebra
1.2K views

11 mn mn

Finance
1.2K views

Using the fama-french 5 facotor model, say you have the value of rit and all the...

Medical Sciences
1.2K views

Imagine if you were walking along the beach and cut the bottom of your foot open...

Biology
1.2K views

SB2 a Which statement best explains the process of transcription as it relates to protein...

Biology
1.2K views

a. Which sex is typically assigned at birth to an individual with XXY chromosomes?b. If...

Basic Math
1.2K views

At the end of 2024 Teal Mountain Co has accounts receivable of 697 200 and...

Statistics
1.2K views

Classify the following statement as an example of classical probability empirical probability or subjective probability...

Calculus
1.2K views

The IVP y 14xy 2x y 0 19 has solution y x

Accounting
1.2K views

Define the difference between direct and indirect cost, variable and fixed cost, and give example...

Accounting
1.2K views

Exercise 22.6 (Algo) Departmental e. allocations LO P2 Gomez Company has two service departments (Personnel...

Accounting
1.2K views

Presented below is information related to Tamarisk Company. Date Ending Inventory (End-of-Year Prices) ...

Accounting
1.2K views

The stockholders' equity section of Cullumber Company consists of common stock ($10 par) $1,500,000 and...