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 = (mν^2)/2
(c) r = (n^2a_0)/z
(d) e = hν
(e) λ = h/(mν)

Answer 1

Equation (a) c = λν describes wavelike behavior, equation (b) to kinetic energy represents particle-like behavior, and equations (d) and (e), involving Planck's constant, describe both as they relate to the wave-particle duality. Option A,B,D,E are correct.

Step-by-step explanation:

The equations that describe particle-like behavior and wavelike behavior pertain to the dual nature of light and matter, recognized in the field of quantum physics. The provided equations can be evaluated based on whether they involve characteristics of waves (such as wavelength and frequency) or properties typically associated with particles (such as mass and energy).

(a) c = λν describes wavelike behavior because it relates the speed of light (c) to wavelength (λ) and frequency (ν), both of which are characteristics of waves.

(b) E = (mν^2)/2 describes particle-like behavior since it represents the kinetic energy (E) of a particle with mass (m) moving with velocity (ν).

(c) r = (n^2a_0)/z pertains to the Bohr model of the atom and reflects a property of electrons in atomic orbits, indicative of particle-like behavior.

(d) E = hν involves both particle-like and wavelike behavior. It equates energy (E) to the product of Planck's constant (h) and frequency (ν), thus describing the energy of a photon, which exhibits wave-particle duality.

(e) λ = h/(mν) describes the de Broglie wavelength, which is the wavelike property of matter, specifically of a particle with mass (m) and velocity (ν). This equation also represents wave-particle duality as it applies to matter.