Which of the following is/are the limitations to the Rutherford's atomic models? I. It is applicable when…

Analysis of the Question

This question tests your understanding of the historical development of atomic theory, specifically the flaws in Ernest Rutherford’s model of the atom (the "planetary model").

Concept Explanation

Rutherford proposed that electrons orbit the nucleus like planets orbit the sun. However, classical physics (Maxwell’s electromagnetic theory) presented two major problems for this model:

1. The Stability Problem: According to classical physics, an accelerating charged particle (like an electron moving in a circular orbit) must continuously radiate energy. If the electron radiates energy, it should lose speed, spiral inwards, and eventually crash into the nucleus. Rutherford’s model could not explain why atoms are stable.
2. The Continuous Spectrum Problem: If the electron were to radiate energy continuously, the spectrum emitted by the atom should be a continuous spectrum (all colors blending into each other). However, experiments showed that atoms emit line spectra (discrete, specific wavelengths).

Because Rutherford’s model assumed continuous radiation, it failed to account for the stability of the atom and the discrete nature of atomic spectra. Bohr later corrected this by proposing that electrons exist in "stationary orbits" where they do not radiate energy.

Step-by-Step Solution

• Statement I: "It is applicable when energy is radiated as electrons are revolving." This is a limitation. Rutherford’s model assumed electrons radiate energy while revolving, which leads to the collapse of the atom. Since atoms don't collapse, this assumption is incorrect.
• Statement II: "It is applicable when energy is radiated in a continuous mode." This is a limitation. Rutherford’s model implies a continuous emission of energy, but experimental evidence shows that atoms emit discrete (line) spectra, not continuous ones.
• Statement III: "It is applicable to an atom with only one electron in the other shell." This is actually a success (or a specific condition) of the Bohr model, not a limitation of Rutherford's. Rutherford's model was fundamentally flawed for all atoms because it couldn't explain stability.

Since Statements I and II describe the theoretical failures (limitations) of the Rutherford model, they are the correct limitations.

Conclusion

The limitations are found in statements I and II. Therefore, the correct option is C.

Exam Tip

When you see questions about atomic models, remember the "Bohr Correction":

• Rutherford: Electrons orbit like planets (failed because it predicted the atom would collapse).
• Bohr: Electrons orbit in fixed energy levels (stationary states) where they do not radiate energy. They only radiate energy when they jump between levels.