Problem 10: Calculate the wavelength of the de Broglie waves associated with electrons accelerated through a potential difference of 200 V.
Solution
De Broglie hypothesis says that all matter has both wave as well as particle nature. The wavelength associated with a particle in motion with momentum p is λ = h/p, where p = mv.
Now to calculate mv, we use the equation ½ mv2 = eV0 and simplifying it as follow,
Multiply both sides by √m.
Now put the values, V0 = 200 V, m = 9.11 × 10-31 kg, e = 1.6 × 10-19 C, we have
Now put this value in the basic de Broglie equation given in the initial para.
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