1.

The kinetic energy of an electron is `4.55 xx 10^(-25)J`. The mass of electron is ` 9.1 xx 10^(-31)kg`. Calculate velocity, momentum and wavelength of the electron.

Answer» Step I. Calculation of the velocity of electron
Kinetic energy `=1//2 m upsilon^(2)=4.55 xx 10^(-25)J=4.55 xx 10^(-25)kg m^(2)s^(-2)`
or ` " " upsilon^(2)=(2xxKE)/(m)=(2xx(4.55 xx 10^(-25) kgm^(2)s^(-2)))/((9.1xx10^(10^(-31)kg)))=10^(6)m^(2)s^(-2)`
or `" " ` Velocity`(upsilon)=(10^(6)m^(2)s^(-2))^(1//2)=10^(3) m s^(-1)`.
Step II. Calculation of momentum of the electron
Momentum of electron `=m upsilon =(9.1 xx 10^(-31) kg)xx(10^(3)ms^(-1))=9.1xx10^(-28)kg ms^(-1)`
Step III . Calculation of wavelength of the electron
According to de Broglie equation :
`lambda =(h)/(m upsilon)= ((6.626 xx 10^(-34)kgm^(2) s^(-1)))/((9.1xx10^(-31)kg)xx(10^(3)m s^(-1)))`
`=0.728 xx 10^(-6)m=7.28 xx 10^(-7)m`


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