An electron and proton are possessing the same amount of kinetic energy. Which of the two have greater wavelength ?

Explanation

The kinetic energy of a particle may be given is :
`E_(k)=(1)/(2) m upsilon^(2)=(1)/(2)(m^(2)upsilon^(2))/(m)=(p^(2))/(2m)`
According to de Broglie equation, `lambda=(h)/(p)" " or" " p=(h)/(lambda)`
On substituting the value of `p, E_(k)=(h^(2))/(2mlambda^(2))`
`E_((ke))=(h^(2))/(2m_(e)lambda_(e)^(2))` (for electron) , `E_(kp)=(h^(2))/(2m_(p)lambda_(p)^(2))` (for proton)
According to available information ,`E_(ke)=E_((kp))`
`:. " " (h^(2))/(2me_(e)lambda_(e)^(2))=(h^(2))/(2m_(p)lambda_(p)^(2)) or lambda_(e)/(lambda_(p))=((m_(p))^(1//2))/(m_(e))^(1//2)`