First slide

Wave nature of matter

Question

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

Moderate

A

E
B

4E
C

3E
D

2E

Solution

$\begin{array}{l} d e B r o g l i e w a v e l e n g t h = λ = \frac{h}{\sqrt{2 E m}} \\ \Rightarrow λ \propto \frac{1}{\sqrt{E}} \\ \Rightarrow E \propto \frac{1}{λ^{2}} \\ I f λ b e c o m e s h a l f, t h e n E b e c o m e s 4 t i m e s . \\ ∴ E_{f} = 4 E_{i} \\ ∴ Δ E = E_{f} - E_{i} = 4 E_{i} - E_{i} = 3 E_{i} \end{array}$

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