Mass ratio of two particles ‘A’ to ‘B’ is 2 : 1. If the velocity of particle ‘A’ is 2×104 m/s and that of particle ‘B’ is 6×104 m/s then the ratio of Debroglie wavelength of ‘B’ to ‘A’ is

Mass ratio of two particles ‘A’ to ‘B’ is 2 : 1. If the velocity of particle ‘A’ is $2 \times 10^{4} m / s$ and that of particle ‘B’ is $6 \times 10^{4} m / s$ then the ratio of Debroglie wavelength of ‘B’ to ‘A’ is

A
1 : 6
B
6 : 1
C
2 : 3
D
3 : 2

Solution:

Debroglie equation;

$λ = \frac{h}{mv}; h is a constant; \frac{λ_{A}}{λ_{B}} = \frac{m_{B} v_{B}}{m_{A} v_{A}}; \frac{λ_{A}}{λ_{B}} = \frac{1 (6 \times 10^{4})}{2 (2 \times 10^{4})}; \frac{λ_{A}}{λ_{B}} = \frac{3}{2};$

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