Question

For electron, proton, deuterium molecule $\left(D_2\right)$ & $\alpha$ - particle a curve between $\lambda$ (De Broglie wavelength) v/s u (speed) is plotted. Select the correct statement(s)

• A. Curve I is for electrons
• B. Curve III is for $\alpha$- particle
• C. Curve I is for proton
• D. Curve III is for Deuterium $\left(D_2\right)$

Answer 1

Answer: (A), (B), (D)

Curve III is for Deuterium $\left(D_2\right)$


According to De-Broglie's hypothesis,
$\lambda =\frac{h}{mu}$, where u is speed
So, at a particular velocity
$\lambda \propto \frac{1}{m}$
Again, an alpha particles contains two protons and two neutrons and similarly deuterium molecule also contains two protons and two neutrons. Mass of proton is also greater than mass of electrons.
Thus, ${\lambda }_{\alpha }={\lambda }_{D_2}<{\lambda }_p<{\lambda }_e$
Hence , ${\lambda }_1$ is for electrons, ${\lambda }_2$ is for protons and ${\lambda }_3$ is for both alpha particles and deuterium molecule