Question

Question:Which of the following equations describe particle-like behavior? Which describe wavelike behavior? Do any

involve both types of behavior? Describe the reasons for your choices.

(a)c=λν

(b)E=mν2

2

(c)r=n2a0

Z

(d)E = hν

(e)λ=h

mν

Short answer

1. wave-like properties
2. particle- like properties
3. wave as well as particle like properties
4. wave-like properties.
5. particle- like properties

Step-by-step solution

determining the behavior of equation given in part (a).

Since, λ in the given equation is wavelength and it is a characteristic property of waves. C = λ v show the wave-like properties.

determining the behavior of equation given in part (b).

Waves are generally defined by radiations and particles defined by mass. In the given equation, m = mass. Hence, the equation displays particle- like properties.

determining the behavior of equation given in part (c).

The equation displays wave as well as particle like properties. Since, radius is a physical quantity determined by a fixed position of an electron at a time. However, there is no mention of mass and velocity hence, it shows both properties.

determining the behavior of equation given in part (d).

In the given equation, E = energy of wave and v = frequency. Hence, it shows wave-like properties.

determining the behavior of equation given in part (e).

The equation displays wave as well as particle- like properties. Since, in the equation,λ is wavelength. However, m = mass and v = velocity.