An electron and a photon each have a wavelength of 1.00 nm. Find
(a) their momentum ,
(b) the energy of the photon and
(c) the kinetic energy of electron.

Explanation

Here `lambda=1.00nm =1xx10^(-9)` m.
(a) Wavelength of electron and photon is same hence according to `p=(h)/(lambda)` their momentum will be equal
`therefore` Equal momentum,
`p=(h)/(lambda)=(6.63xx10^(-34))/(1xx10^(-9))`
`therefore p=6.63xx10^(-25)kg ms^(-1)`
(b)Energy of photon,
`E=(hc)/(lambda)=(6.63xx10^(-34)xx3xx10^(8))/(1xx10^(-9))`
`therefore E=19.89xx10^(-17)J`
`therefore E=(19.89xx10^(-17))/(1.6xx10^(-19))eV`
`therefore E=12.43xx10^(2)eV`
`~~1.243.10^(3)eV`
(C )Kinetic energy of electron,
`K=(p^(2))/(2m)=((6.63xx10^(-25))^(2))/(2xx9.1xx10^(-31))=(43.9569xx10^(-5))/(18.2xx10^(-31))`
`thereforeK=2.4152xx10^(-19)J`
`therefore=(2.452xx10^(-19))/(1.6xx10^(-19))eV`
`=1.509eV~~1.51 eV`