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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 $=2u$
$V _{ D }=5 V_{\alpha}$
$\lambda_{ D }=\frac{1}{2 \times V _{ D }}, \lambda_{\alpha}=\frac{1}{4 V _{\alpha}}$
$\frac{\lambda_{ D }}{\lambda_{\alpha}}=\frac{4 V _{\alpha}}{2 V _{ D }}$