Dual Nature Of Matter Question 2
Question 2 - 24 January - Shift 2
An $\alpha$-particle, a proton and an electron have the same kinetic energy. Which one of the following is
correct in case of their De-Broglie wavelength:
(1) $\lambda _{\alpha}>\lambda_p>\lambda_e$
(2) $\lambda _{\alpha}<\lambda_p<\lambda_e$
(3) $\lambda _{\alpha}=\lambda_p=\lambda_e$
(4) $\lambda _{\alpha}>\lambda_p<\lambda_e$
Show Answer
Answer: (2)
Solution:
Formula: De Broglie wavelength
$\lambda_D=\frac{h}{p}=\frac{h}{\sqrt{2 mK}}$
$\therefore \lambda \propto \frac{1}{\sqrt{m}}$
$\because m _{\alpha}>m_p>m_e$
$\lambda_e>\lambda_p>\lambda _{\alpha}$
