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

We are given that
Kinetic energy f electron `= 3. 0 xx 10 ^(-25) J.`
We are to find out the wavelength of an electron.
We know that `K. E. = (1)/(2) mv ^(2)`
or `v = sqrt ((2 K. E. )/( m ))" "...(i)`
From de-Broglie eq.
`lamda = ( h)/(mv)" "..(ii)`
Subsituating the value of v from eq. (i) in eq. (ii), we get
`lamda = (h)/( m sqrt ((2 K. E. )/( m )))`
`or lamda = (h)/(sqrt ( 2m K. E. ))`
`lamda = ( 6.626 xx 10 ^(-34) Js )/( sqrt (2 xx 9.1 xx 10 ^(-31) xx 3. 0 xx 10 ^(-25)))= ( 6.66 xx 10 ^(-34))/( sqrt ( 54. 6 xx 10 ^( - 56)) )= ( 6.6 xx 10 ^(- 34))/( 7. 39 xx 10 ^(-56)) = 0.8967 xx 10 ^(-6)`
`lamda = 8967 Å`