He+ ions are accelerated by an applied voltage, gaining kinetic energy of ??=12??2=??KE=12mv2=eV, where ?v is the velocity, ?e is the elementary charge = 1.602E-19 C, and ?V is the applied voltage. Assuming the mass of an He+ ion is 4.003 amu, what voltage should be used to accelerate the He+ ions to achieve a DeBroglie wavelength of 1 pm (1E-12 m)?
To minimize problems associated with charging and damage during imaging, He ion microscopy is sometimes used for imaging biological samples instead of electron microscopy. In this imaging technology, He+ ions are accelerated by an applied voltage, gaining kinetic energy of ??=12??2=??KE=12mv2=eV, where ?v is the velocity, ?e is the elementary charge = 1.602E-19 C, and ?V is the applied voltage. Assuming the mass of an He+ ion is 4.003 amu, what voltage should be used to accelerate the He+ ions to achieve a DeBroglie wavelength of 1 pm (1E-12 m)?
Hint: before putting in numbers, derive an equation for the voltage, ?V, in terms of the other variables and constants.
Hint #2: include conversion of mass to kg in your calculation!
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