What is the de Broglie wavelength of an electron whose kinetic energy is 120 eV?  (Answer: 1.12 ｘ10⁻¹⁰ m)



Given Data:

Kinetic Energy = K.E = 120  eV = 120ｘ 1.6 ｘ 10⁻¹⁹ J = 192 ï½˜ 10⁻¹⁹ J

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

∴ Plank's Constant = h =  6.626 ｘ 10⁻³⁴ m² kg s⁻¹

To Find:

De Broglie Wavelength = λ =  ? 




Solution:


We know that momentum P is given by

P = `\frac {h}{λ}`


or


λ = `\frac {h}{P}`


but P = mv , So


λ = `\frac {h}{mv}` ------------(1)


But the value of speed v is unknown so, to find its value we have the formula of K.E


`\frac {1}{2}` mv² = K.E

or

v² = `\frac {2 K.E}{m}`

or

v = `\sqrt frac {2 K.E}{m}`


by putting values


v = `\sqrt frac {2 ｘ 192 ｘ 10⁻¹⁹ J}{9.11 ｘ 10⁻³¹ kg}`


v = `\sqrt frac {384 ｘ 10⁻¹⁹ J}{9.11 ｘ 10⁻³¹ kg}`

v = `\sqrt {42.151 ｘ 10¹² m² s⁻²}`


v = 6.492ｘ 10⁶ m s⁻¹


Now putting all the corresponding values in equation (1)

λ = `\frac {6.626 ｘ 10⁻³⁴ m² kg s⁻¹}{9.11 ｘ 10⁻³¹ kg ｘ 6.492ｘ 10⁶ m s⁻¹}`


λ = `\frac {6.626 ｘ 10⁻³⁴ m² kg s⁻¹}{59.142 ｘ 10⁻²⁵ kg m s⁻¹}`

λ = 0.112 ï½˜ 10⁻⁹ m

or

λ = 1.12 ï½˜ 10⁻¹⁰ m -------------Ans.

[10⁻¹⁰ m = A°] 

λ = 0.867 A° --------------------Ans.


------------------------------------------------------------

Similar Question:



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

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.