The mass of an electron is `9.1 xx 10^(-25)J`, if its K.E. is `3.0 xx 10^(-25)J`. Calculate its wavelength.

Explanation

Step I. Calculation of velocity of velocity of the electron
Kinetic energy`1//2 m upsilon^(2)=3.0xx10^(-25)J=3.0xx10^(-25)kg m^(2) s^(-2)`
`upsilon^(2)=(2xxK.E.)/(m)=(2xx(3.0xx10^(-25) kg m^(2) s^(-2)))/((9.1xx10^(-31)kg))=65.9xx10^(4)m^(2)s^(-2)`
`upsilon = (65.9xx10^(4)m^(2)s^(-2))^(1//2)=8.12xx10^(2) ms^(-1)`
Step II. Calculation of wavelength of the electron
According to de Broglie's equation,
`lambda=(h)/(m upsilon)=((6.626xx10^(-34) kg m^(2) s^(-1)))/((9.1xx10^(-31)kg)xx(8.12xx10^(2)ms^(-1)))`
`=0.08967xx10^(-5)m=8967xx10^(-10)m=8967Ã…. " " (.:'Ã…=10^(-10)m)`