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Physics · 2022 · 3 marks
CBSE 2022 · Region 4 · Set 2 · Q8
The wavelength of the waves associated with a particle having kinetic energy E is λ. How and by what factor should its kinetic energy be changed so…
The wavelength of the waves associated with a particle having kinetic energy E is $\displaystyle \lambda$. How and by what factor should its kinetic energy be changed so that the wavelength becomes $\displaystyle \left(\frac{\lambda}{2}\right)$ ? Also, find the ratio of the final to the initial velocity of the particle.
Marking-scheme solution
$\displaystyle \lambda = \dfrac{h}{\sqrt{2mE_1}}$$\displaystyle \dfrac{\lambda}{2} = \dfrac{h}{\sqrt{2mE_2}}$$\displaystyle E_2 = 4E_1$$\displaystyle \lambda = \dfrac{h}{mv}$$\displaystyle \lambda \propto \dfrac{1}{v}$$\displaystyle \dfrac{v_f}{v_i} = \dfrac{2}{1}$
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