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Dual Nature of Radiation and Matter — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsDual Nature of Radiation and Matter1 Mark
Question
For question two statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions front the codes (a), (b), (c) and (d) as given below.
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is NOT the correct explanation of A.
  3. A is true but R is false.
  4. A is false and R is also false.
Assertion (A): The de-Broglie wavelength of a neutron when its kinetic energy is K is $\lambda$. Its wavelength is $2\lambda$, when its kinetic energy is 4K.
Reason (R): The de-Broglie wavelength $\lambda$ is directly proportional to square root of the kinetic energy.
✓

Answer

  1. A is false and R is also false.

Explanation:

$\lambda=\frac{\text{h}}{\sqrt{2\text{mk}}},\text{i.e.,}\lambda\propto\frac{1}{\sqrt{\text{K}}}$

$\therefore\frac{\lambda'}{\lambda}=\sqrt{\frac{\text{K}}{\text{K}'}}=\sqrt{\frac{\text{K}}{4\text{K}}}=\frac{1}{2}$ or $\lambda'=\frac{\lambda}{2}$

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