Question

Select the correct answer. which restricted domain would allow you to define the inverse cosine function? a. [ 0 , π ] b. [ - π , π ] c. [ - π 2 , π 2 ] d. [ 0 , 1 ]

Answer 1

The de Broglie wavelength of an electron determines its wave-like behavior. The option 0.5λ would be disallowed, while the option λ would be allowed.

Step-by-step explanation:

The de Broglie wavelength is given by the equation λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle. For an electron, the de Broglie wavelength determines its wave-like behavior. In the context of the question, we are considering the orbital circumference of the electron within the atom.

Option a. 0.5λ represents half of the de Broglie wavelength. This would mean that the orbital circumference is smaller than the wavelength. Since the orbital circumference should be a whole number of wavelengths, 0.5λ would not be allowed.

Option b. λ represents the full de Broglie wavelength. This would allow for a whole number of wavelengths in the orbital circumference and is therefore allowed.