Graphs of de Broglie wavelength ( ) versus 1 V (where V is the accelerating potential) are plotted for a proton and an alpha particle. Both plots are straight lines passing through the origin. The ratio of the slope of the graph for the proton to the slope of the graph for the alpha particle is

Step-by-step solution

The de Broglie wavelength of a charged particle accelerated through a potential V is given by = h 2mqV Rearranging this, we get = ( h 2mq ) 1 V Thus, the slope of the versus 1 V graph is S = h 2mq For a proton, mass m_p = m and charge q_p = e . The slope is S_p = h 2me For an alpha particle, mass m_ = 4m and charge q_ = 2e . The slope is S_ = h 2(4m)(2e) = h 16me = 1 2 2 h 2me Taking the ratio of the slopes: S_p S_ = 1 ( 1 2 2 ) = 2 2 The ratio is 2 2 : 1 . Answer: 2 2 : 1