Question

The ratio of de Broglie wavelengths of a deuterium atom to that of an α - particle, when the velocity of the former is five times greater than that of later, is
a) 4
b) 0.2
c) 2.5
d) 0.4

Answer 1

According to De- broglie wavelength , λ = h/mv
where λ is wavelength, h is plank's Constant, m is mass and v is velocity of particle.

For Deuterium ,
mass of Deuterium = 2 a.m.u
speed of Deuterium = v
so, wavelength of Deuterium = h/2v -----(1)

For alpha - particle,
Mass of alpha particle = 4 a.m.u
speed of alpha particle = v/5
so, wavelength of alpha particle = h/4.v/5 = 5h/4v ----(2)

Now, ratio of wavelength of Deuterium to alpha particle = h/2v/5h/4v
= 4/10 = 0.4

Hence , option (d) is correct