Test: Dual Nature of Matter - JEE MCQ

and as we know 1Å = 0.1 nm, so 1.227Å = 0.122 nm

The Davisson-Germer experiment demonstrated the wave nature of the electron, confirming the earlier hypothesis of deBroglie. Putting wave-particle duality on a firm experimental footing, it represented a major step forward in the development of quantum mechanics. The Bragg law for diffraction had been applied to x-ray diffraction, but this was the first application to particle waves.

The de-broglie equation states, mv=h/l

= v=h/lm

the velocity here is inversely dependant on the masses.

Higher the mass lower will be the velocity.

Therefore, electron will have a higher velocity to produce matter waves of same wavelength.

We have mass – a particle property, in the same equation as wavelength – a wave property. Thus if matter exhibits wave properties, it must be given by equation (3). Equation (3) is the de Broglie equation and represents the wave-particle duality. Hence we say that everything in the Cosmos exhibits a dual nature.

Mass of alpha(a)= 4.
mass of deutron(d) =2.
wavelength=h/mv
Potential are same of both particle so their speed will be same . 
Here, wavelength is inversely proportional to mass
so,
wavelength of alpha/wavelength of deutron = mass of deutron /mass of alpha.= 2/4=1/2

De Broglie wavelength = h/mv,
where h = plancks constant, mv = momentum.
As they move with same momentum, de Broglie wavelength remains constant for all.

The variable v can either be taken to be the speed of the particle or the group velocity of the corresponding matter wave. Since the particle speed for any particle that has mass (according to special relativity), the phase velocity of matter waves always exceeds c, i.e.

There is a direct relation ,
energy= 12400/wavelength(i e ,lambda in angstroms).
given E= 1k e v = 1000 e.v
wavelength = 12400/1000
wavelength= 124/10
wavelength= 12.4

λ=h/P
Here P= √2mk
K=kinetic energy
λ=h/√2mk
By energy conversion
K=eV_s
λ=h/√2m_eV_s
√V_s=h/ λ√2me
V_s=h²/ λ2me
V_s=(6.626x10^-34)²/(1x10^-9)²x2x9.11x10^-31xe
Where e=1.602x10^-19
V_s=43.9x10^-68/29.1x10^-68
   =1.508v
V_s=1.5v