A particle moving with kinetic energy E has de Broglie wavelength λ. If energy E is added to its energy, the wavelength become λ/2. Value of E, is :

Engineering

Physics

de Broglie Hypothesis and Dual Nature

Question

A particle moving with kinetic energy E has de Broglie wavelength λ. If energy $∆$ E is added to its energy, the wavelength become λ/2. Value of $∆$ E, is :

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$λ = \frac{h}{\sqrt{2 (KE) m}} \Rightarrow λ \propto \frac{1}{\sqrt{KE}}$

$\frac{λ}{λ / 2} = \sqrt{\frac{{KE}_{f}}{{KE}_{i}}}$

4KE_i = KE_f

⇒ $∆$ E = 4KE_i – KE_i = 3KE = 3E