Question

Which of the following describes one of the main features of wave-particle duality?

a. as speed increases, the wave nature matter becomes more evident
b. as momentum decreases, the particle nature of the matter becomes more evident
c. as energy increases, the wave nature of matter becomes easier to observe
d. as mass increases, the wave nature of matter is less easy to observe.

Answer 1

Answer: as mass increases, the wave nature of matter is less easy to observe.

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
`\lambda` is given by the following formula:

`\lambda=(h)/(p)` (1)

Where:

`h` is the Planck constant

`p` is the momentum of the atom, which is given by:

`p=m.v` (2)

Where:

`m` is the mass

`v` is the velocity

Substituting (2) in (1):

`\lambda=(h)/(m.v)[\tex]  <strong> (3)</strong></p><p></p><p>As we can see, <strong>if we increase the mass, the wavelength decreases </strong>(because [tex]\lambda` is inversely proportional to
`m`).

Therefore, if the wavelength decreases the wave nature of matter is less easy to observe.

The other options are incorrect because:

a) as
`v` increases
`\lambda` decreases and the particle nature matter becomes more evident

b) as
`p` decreases
`\lambda` increases and the wave nature matter becomes more evident

c) There is also a relation between the wavelength and the energy
`E`:

`\lambda=(hc)/(E)`

So, as energy increases, the particle nature matter becomes more evident and the wave nature of matter becomes harder to observe