Single Choice

If the momentum of an electron is changed by P, then the de-Broglie wavelength associated with it changes by 0.5%. The initial momentum of an electron will be:

A$$400P$$
B$$\dfrac{P}{200}$$
C$$100P$$
D$$200P$$
Correct Answer

Solution

According to de-Broglie relation:

$$\lambda = \dfrac{h}{p}$$

let initial momentum $$=p_1$$ and associated wavelength is $$\lambda_1$$

and with a decrease in wavelength momentum will increase

thus $$\Delta p=-P$$ for $$\Delta \lambda=\dfrac {0.5}{100}\times \lambda_1$$

diffrentiating the debroglie relation we get:

$$\dfrac { \Delta \lambda }{\lambda_1}=-\dfrac{ \Delta p }{p_1}$$

and $$\dfrac { 0.005\times \lambda_1 }{\lambda_1}=\dfrac{ P }{p_1}=\dfrac{0.5}{100}$$
$$p_1=200P$$

option D is correct

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