Q160 / 160 · WBJEE 2015 · Physics

Consider two particles of different masses, In which of the following situations the heavier of the two particles will have smaller de-Broglie wavelength?

  • Correct answer
    A
    Both have a free fall through the same height
  • Correct answer
    B
    Both move with the same kinetic energy
  • C
    Both move with the same linear momentum
  • Correct answer
    D
    Both move with the same speed

Solution

The de-Broglie equation is $$ \begin{aligned} \lambda &=\frac{h}{m v}=\frac{h}{\sqrt{2 m k}} \Rightarrow m=\frac{h}{\lambda v} \\ \Rightarrow \quad m \propto \frac{1}{\lambda}, \text { if } \frac{h}{v} &=\mathrm{constant} \end{aligned} $$ Again, $\frac{h}{v}$ will be constant only when $v$ is constant Thus, in present case the de-Broglie wavelength of heavier particle will be smaller. When the velocities of two particles will be same or both move with same kinetic energy(K).

Hence, the correct answer is options: 'A', 'B', 'D'.

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