Final answer:
Rutherford's model couldn't explain the specific wavelengths of light an atom emits, implying electrons should collapse into the nucleus, which does not happen. Niels Bohr resolved this by proposing quantized orbits for electrons. His model explained hydrogen's spectrum but later models showed that specific orbits were a simplification.
Step-by-step explanation:
The Problem with Rutherford's Model and Bohr's Solution
The problem with Rutherford's atomic model was that it could not explain why atoms emit light at specific wavelengths or frequencies. This issue is rooted in the fact that, according to Maxwell's theory of electromagnetic radiation, electrons changing their path should emit energy. In a planetary model, this would lead to the electrons spiraling into the nucleus, resulting in the atom collapsing. This clearly does not happen in reality, as we do not observe atoms spontaneously collapsing. Moreover, the model couldn't describe the unique atomic spectra of different elements, which are like their fingerprints in terms of light emission.
Niels Bohr resolved this by suggesting that electrons can only orbit the nucleus in certain quantized orbits or energy levels. By doing so, he explained the atomic spectrum of hydrogen and established new principles in quantum mechanics that allowed for only specific energy levels and corresponding spectral lines, thus avoiding the paradox of the atom collapsing.
Unfortunately, Bohr's model had its own limitations, as it could not be extended to more complex atoms such as helium, and it still held on to the idea of specific orbits which later quantum mechanics showed to be a simplification not fully consistent with the behavior of subatomic particles.