The allowed orbits for the electron around the nucleus of the hydrogen atom are explained by de Broglie as ...
a. Quantized values for the total energy of the electron in the atom
b. Quantized values for the angular momentum of the electron in the atom
c. Standing waves for the electron when considered as a matter-wave
d. Wavelengths of the electromagnetic spectrum where the atom will absorb or emit radiation
e. Experimental errors in low-precision experiments
http://tinyurl.com/yhmt8qx
Read what DeBroglie said.
Now the answer. I think c is the better answer, however, a is essentially the same thing, if you read DeBroglie's words. It would take a politician's logic to separate those concepts. If I were the instructor, I wouldn't mark either wrong.
To determine which option is correct, we need to understand de Broglie's explanation of the allowed orbits for the electron around the nucleus of the hydrogen atom.
de Broglie's proposal is based on the concept of wave-particle duality. According to de Broglie, particles like electrons also exhibit wave-like properties. He suggested that particles, including electrons, can behave as both particles and waves simultaneously.
Based on this idea, de Broglie's explanation for the allowed orbits of the electron in the hydrogen atom is described by option (c): Standing waves for the electron when considered as a matter-wave.
To arrive at this conclusion, de Broglie's principle relates the wavelength (λ) of a particle to its momentum (p). For an electron in a hydrogen atom, the allowed electron orbits would correspond to standing waves that fit within the circumference of the orbit. These standing waves have specific wavelengths and determine the energy levels available to the electron. Only certain discrete wavelengths (corresponding to discrete energy levels) are allowed, which results in quantized values for the total energy of the electron (option a) and quantized values for the angular momentum of the electron (option b).
Regarding option (d), although de Broglie's concept of matter waves relates the wavelength of a particle to its energy, it is not specifically focused on absorption or emission of radiation by the atom. This option is more closely related to the Bohr model of the atom.
Option (e), experimental errors in low-precision experiments, is unrelated to de Broglie's explanation and is likely included as a distractor.
In summary, de Broglie's explanation of the allowed orbits for the electron in the hydrogen atom is based on the concept of standing waves for the electron as a matter-wave (option c).