Find the energy required by an electron to have its de Broglie wavelength reduced from `10^(-10)m " to " 0.5 xx 10^(-10)m`.

Explanation

de Broglie wavelength,
`lamda = (h)/(p) = (h)/(sqrt(2mE))`
or, `2mE = (h^(2))/(lamda^(2)) or, E = (h^(2))/(2m).(1)/(lamda^(2))`
`:.` Energy required by the electron,
`E_(2) - E_(1) = (h^(2))/(2m) ((1)/(lamda_(2)^(2)) - (1)/(lamda_(1)^(2)))`
`= ((6.62 xx 10^(-34))^(2))/(2 xx 9.1 xx 10^(-31)) . [(1)/((0.5 xx 10^(-10))^(2)) - (1)/((10^(-10))^(2))]`
`= 7.2 xx 10^(-17)J`
`:. E_(2) - E_(1)= (7.2 xx 10^(-17))/(1.6 xx 10^(-19)) eV = 450 eV`