The ratio of de-Broglie wavelength of two particles A and B is 2: 1 . If the velocities of A and B are 0.05 ~ms ⁻¹ and 0.02 ~ms ⁻¹ , respectively, then the ratio of their masses m_A: m_B must be

Step-by-step solution

According to de-Broglie's wavelength, = h m v Now, de-Broglie's wavelength of particle A is _A= h m_A v_A Similarly, de-Broglie's wavelength of particle B is _B= h m_B v_B Ratio of de-Broglie wavelength of A and B is 2: 1 i.e., aligned _A _B & = h m_A v_A m_B v_B h 2 1 & = h m_A 0.05 m_B 0.02 h 2 1 & = m_B 0.02 m_A 0.05 2 0.02 & = m_B m_A 0.05 1 0.01 & = m_B m_A 0.05 m_A m_B = 1 5 aligned Hence, the ratio of their masses m_A: m_B is 1: 5 .