The mass of an electron is ` 9. 1 xx 10^(-31) kg`. If its K.E. is `3. 0 xx 10 ^(25) J`. Calculate its wavelength .

Explanation

from de Broglie's equation
`lambda= h/(mv)`
given
kinetic energy (K.E) of the electron =`3.0 xx 10^(-25)J`
since ` K.E =1/2 mv^(2)`
velocity (v) = `sqrt(2K.E)/m`
` sqrt(2(3.0xx10^(-25)J))/(9.10939xx10^(-31)g)`
`sqrt(6.5866xx10^(4)`
`v=811.579 ms^(-1)`
subsitiuing the value in the expression of `lambda`
`lambda =(6.626xx10^(-34) Js)/((9.10939xx10^(-31) kg) (811.5790 ms^(-1)))`
`lambda = 8.9625xx 10^(-7) m`
Hence, the wavelength of the electron is `8.9625 xx 10^(-7) m `.