Find the wavelength associated with an electron in the state n=4 of hydrogen. (Answer: 1.33 nm) 



Given:

Atom: Hydrogen

Energy level n = 4

∴ Plank's Constant = h =  6.62 ｘ 10⁻³⁴ m² kg s⁻¹

∴ Mass of the electron = m = 9.11 ｘ 10⁻³¹ kg

∴ Charge on the electron = e = 1.6 ｘ 10⁻¹⁹ C

∴ Coulomb's Constant  = K = 9 ｘ 10⁹ N m² C⁻²


To Find:


The wavelength associated with electron = λ =  ?


Solution:

The  formula for wavelength is 

 λ = h√2mEn

Where

En = 2π²k²me⁴n²h²  So,

 λ = h√2m2π²k²me⁴n²h²

 λ = h2mπke²nh

or

 λ = nh²2mπke²

by putting the corresponding values 



 λ = 4ｘ(6.62ｘ10⁻³⁴m²kgs⁻¹)²2ｘ9.11ｘ10⁻³¹kgｘ3.1416ｘ9ｘ10⁹Nm²C⁻²ｘ(1.6ｘ10⁻¹⁹C)²


 λ = 4ｘ43.8244ｘ10⁻⁶⁸m⁴kg²s⁻²515.159568ｘ10⁻²²kgNm²C⁻²ｘ2.56ｘ10⁻³⁸C²

[N = kg m s⁻²]

 λ = 175.2976ｘ10⁻⁶⁸m⁴kg²s⁻²1318.80849408ｘ10⁻⁶⁰kgms⁻²ｘkgm²

or

 λ = 0.1329ｘ 10⁻⁸ m

or

 λ = 1.329ｘ 10⁻⁹ m

Or

 λ = 1.329 nm  ---------------Ans.

Thus the wavelength associated with an electron in the state n=4 of hydrogen is 121.9  nm  



************************************

Shortcut Links For 


1. Website for School and College Level Physics   
2. Website for School and College Level Mathematics  
3. Website for Single National Curriculum Pakistan - All Subjects Notes 

© 2022-Onwards by Academic Skills and Knowledge (ASK)     

Note:  Write me in the comment box below for any query and also Share this information with your class-fellows and friends.