Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The ratio of de-broglie wavelength of a deuterium atom to that of a-particle when the velocity of former is five times greater than that of latter is:

Structure of Atom

Solution:

$\lambda=\frac{ h }{ mv }$

mass of $\alpha$ -particle $=4u$, mass of deuterium $=2u$

$V _{ D }=5 V_{\alpha}$

$\lambda_{ D }=\frac{1}{2 \times V _{ D }}, \lambda_{\alpha}=\frac{1}{4 V _{\alpha}}$

$\frac{\lambda_{ D }}{\lambda_{\alpha}}=\frac{4 V _{\alpha}}{2 V _{ D }}$

$=\frac{4}{2 \times 5}=\frac{4}{10}=0.4$