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 mv^{2} = eV_{0} and simplifying it as follow,

Multiply both sides by √m.

Now put the values, V_{0} = 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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