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Physics Question on Dual nature of matter

If the momentum of an electron is changed by P, then the de Broglie wavelength associated with it changes by1% 1\%. The initial momentum of the electron will be:

A

200 P

B

100 P

C

300 P

D

150 P

Answer

100 P

Explanation

Solution

 The de Broglie wavelength is given by λ=hp, where p is the momentum.  A 1% change in wavelength corresponds to a 1% change in momentum.  If the change in momentum is P, the initial momentum p0 is given by:\text{ The de Broglie wavelength is given by } \lambda = \frac{h}{p}, \text{ where } p \text{ is the momentum.} \\\ \text{ A 1\% change in wavelength corresponds to a 1\% change in momentum.} \\\ \text{ If the change in momentum is } P, \text{ the initial momentum } p_0 \text{ is given by:}

Pp0=0.01  ⟹  p0=100P\frac{P}{p_0} = 0.01 \implies p_0 = 100 P