Particle $A$ of mass $m_A=\frac{m}{2}$ moving along the $x-$ axis with velocity $\mathrm{v}_0$ collides elastically with another particle $B$ at rest having mass $m_B=\frac{m}{3}$. If both particles move along the $x$-axis after the collision, the change $\Delta \lambda$ in de-Broglie wavelength of particle A, in terms of its de-Broglie wavelength ( $\lambda_0$ ) before collision is