An electron beam can undergo diffraction by crystals. Through what potential should a beam of electrons be accelerated so that its wavelenegth becomes equal to 1.54 Å?

An electron beam can undergo diffraction by crystals. Through what pot

1.	An electron beam can undergo diffraction by crystals. Through what potential should a beam of electrons be accelerated so that its wavelenegth becomes equal to 1.54 Å?
Answer» Solution :The aim is to find the energy of the electron in electron volts (eV). As K.E. `= (1)/(2) MV^(2)`, therefore, first we calculate velocity of the electron to have a wavelength of `1.54 Å`. Applying de BROGLIE equation `lamda = (h)/(mv)` `v = (h)/(m XX lamda) = ((6.62 xx 10^(-34) kg m^(2) s^(-1)))/((9.1 xx 10^(-31) kg) (1.54 xx 10^(-10) m)) = 4.72 xx 10^(6) m s^(-1)` Now, K.E. `= (1)/(2) mv^(2) = (1)/(2) (9.1 xx 10^(-31)kg) (4.72 xx 10^(6) ms^(-1))^(2) = 1.01 xx 10^(-17) kg m^(2) s^(-2)` `= 1.01 xx 10^(-17) J " " ( :' 1J = 1 kg m^(2) s^(-2))` `= (1.01 xx 10^(-17))/(1.602 xx 10^(-19)) eV " " ( :' 1 eV = 1.602 xx 10^(-19) J)` `= 63.12 eV` Hence, potential required = 63.12 volts