At the beginning of the 20th century the French physicist Louis De Broglie proposed the existence of matter waves, that is to say that all matter has a wave associated with it.
In this sense, the de Broglie wavelength [tex]\lambda[/tex] is given by the following formula:
[tex]\lambda=\frac{h}{p}[/tex] (1)
Where:
[tex]h[/tex] is the Planck constant
[tex]p[/tex] is the momentum of the atom, which is given by:
[tex]p=m.v[/tex] (2)
Where:
[tex]m[/tex] is the mass
[tex]v[/tex] is the velocity
Substituting (2) in (1):
[tex]\lambda=\frac{h}{m.v}[\tex] (3)
As we can see, if we increase the mass, the wavelength decreases (because [tex]\lambda[/tex] is inversely proportional to [tex]m[/tex]).
Therefore, if the wavelength decreases the wave nature of matter is less easy to observe.
The other options are incorrect because:
a) as [tex]v[/tex] increases [tex]\lambda[/tex] decreases and the particle nature matter becomes more evident
b) as [tex]p[/tex] decreases [tex]\lambda[/tex] increases and the wave nature matter becomes more evident
c) There is also a relation between the wavelength and the energy [tex]E[/tex]:
[tex]\lambda=\frac{hc}{E}[/tex]
So, as energy increases, the particle nature matter becomes more evident and the wave nature of matter becomes harder to observe
