What is the wavelength of an electron with a velocity of #3.85xx10^6" m/s"#?

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Answer 1 · 2014-11-04T01:19:58

The wavelength of an electron with a velocity of #3.85xx 10^6# #"m/s"# is #1.89xx10^(-10)# #"m"#.

The de Broglie equation relating the wavelength of an electron to its velocity is:

#lambda# = #h/p#

where

#lambda= "wavelength in m"#

#p = "momentum"= mv#,

where:

#m= "kg"#, and #v = "m/s"#

Known/Given:

Planck's constant, #6.626xx10^(-34)"J"*"s"#

velocity of electron, #3.85 xx10^6"m/s"#

mass of electron, #9.109xx10^(-31)"kg"#

Unknown:

momentum #(p)#

wavelength #(lambda)#

Equations:

#p# = #mv#

#lambda# = #h/p#

Solution:

1. Calculate momentum.

#p = (9.109xx10^(-31)"kg")xx(3.85xx10^6"m/s")= 3.507xx10^(-24)"kg"*"m/s"#

2. Calculate wavelength:

#lambda=(6.626xx10^(-34)"J"*"s")/(3.507xx10^(-24)"kg"*"m/s")=1.89xx10^(-10)# #"m"#. (rounded to three significant figures)

Because #"1 Joule"= "1 kg"*"m"^2/("s"^2)#, kilograms and seconds cancel, leaving meters.

Answer:
The wavelength of an electron with a velocity of #3.85xx 10^6# #"m/s"# is #1.89xx10^(-10)# #"m"#.