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 the velocity of electron
Kinetic energy `= 1//2 m upsilon^(2)= 3.0 xx 10^(-25) kg m^(2) s^(-2))`
` upsilon ^(2)= ( 2xx K.E.)/(m)=(2xx (3.0 xx 10^(-25)kg m^(2) s^(-2)))/((9.1 xx 10^(-31) kg))= 65.9 xx 10^(4) m^(2) s^(-2)`
` upsilon =(65.9 xx 10^(4) m^(2) s^(-2)) ^(1//2)=8.12 xx 10^(2) m s^(-1)`
Step II. Calculation of the wavelength of electron
According to be Broglie's equation,
` lambda=(h)/( m upsilon)=((6.62 xx 10^(-34) kg m^(2) s^(-1)))/((9.1 xx 10^(-31) kg) xx ( 8.12 xx 10^(2) ms^(-1)))`
`=0.0896 xx 10^(-5)m = 8960 xx 10^(-10)m = 8960 Ã…. " "` (`:. 1 Ã… = 10 ^(-10)m`)