The kinetic enegry of a moving electron is `3.0 xx 10^(-25)J`. Calculate its wavelength.

Options

A. `786 nm`
B. `520 nm`
C. `897 nm`
D. `623 nm`

Answer

C

Explanation

First we calculate the velocity of the moving electron. Since `KE = (1)/(2)mV^(2)`
`V = sqrt((2KE)/(m)) = sqrt(((2)(3.0xx10^(-25)kgm^(2)s^(-1)))/((9.1xx10^(-31)kg)))`
`=812 ms^(-1)`
According to de Broglie's relationship,
`lambda = (h)/(mv)`
`= ((6.63xx10^(-34) kg m^(2) s^(-1)))/((9.1xx10^(-31) kg)(812ms^(-1)))`
`= 0.000897 xx 10^(-3)m = 8.97 xx 10^(-7)m = 897 nm`