The formula to calculate the de Broglie wavelength of the proton is given by
λp=2mpqpVh...(1)
The formula to calculate the de Broglie wavelength of the alpha particle is given by
λα=2mαqαV′h...(2)
Divide equation (1) by equation (2) and simplify to obtain the required ratio.
λαλp=mpmα×qpVqαV′...(3)
Substitute the values of the known parameters into equation (3) to calculate the required ratio.
λαλp==14×1×22×44:1