A proton and an α-particle have the same de-Broglie wavelength. Determine the ratio of (i) their accelerating potentials (ii) their speeds.

De-broglie wavelength of the particle is given by, 

;

where V= Accelerating potential and v is the speed of the particle. 

Given that, the de-broglie wavelength is the same for both proton and a-particle.

Charge on  particle = 2 q_p;
Mass of -particle = 4 m_p 

Charge on proton= q_p; 
Mass of proton =  m_p 

2:1 is the required ratio of the accelerating potential.

Also, 



4:1 is the required ratio of the speed of proton to the speed of alpha-particle.