Th velocities of two particle A and B are `0.05` and 0.02 ms6(-1)` respectively. The mass of B is five times the mass of A.The ratio of their De-Broglie wavelength is

Options

A. `2:1`
B. `1:4`
C. `1:1`
D. `4:1`

Answer

a

Explanation

Velocity of particle A,`V_A=0.05 ms^(1)`
Velocity of particle B,`V_B=0.02 ms^(-1)`
mass of particle `A=m_A`
Mass of particle `B=m_B=5m_A`
From De-Broglie.s relation,`lambda=(h)/(mv)`
For particle A,`lambda_A=(h)/(m_Axx0.02)`
for particle B,`lambda_A=(h)/(m_Bxx0.03)=(h)/(5m_Axx0.02)`
`lambda_A/lambda_B=((h))/((m_Axx0.05)/((h)/(5m_Axx0.02)=(h)/(m_Axx0.05)xx(5m_Axx0.02)/(h)`
`lambda_A/lambda_B=(5xx0.02)/(0.05)=2/1`
`lambda_A:lambda_B=2:1`