Explain Bohr's atomic model postulates and shortcomings. Calculate the longest wavelength in the Balmer series.

• Electrons revolve around the nucleus in specific circular orbits called stationary states without radiating energy.
• Electrons can only exist in orbits where their angular momentum is an integral multiple of $\frac{h}{2\pi}$, i.e., $mvr = n\frac{h}{2\pi}$.
• Energy is absorbed when an electron jumps from a lower energy orbit to a higher energy orbit, and energy is emitted when it jumps from a higher energy orbit to a lower energy orbit. The energy difference is given by $\Delta E = E_2 - E_1 = h\nu$.

• It could only explain the spectra of hydrogen and hydrogen-like ions (e.g., $He^+$, $Li^{2+}$) but failed for multi-electron atoms.
• It could not explain the splitting of spectral lines into finer lines in the presence of a magnetic field (Zeeman effect) or an electric field (Stark effect).
• It did not account for the wave nature of electrons (de Broglie hypothesis) or the Heisenberg uncertainty principle.

Water ($H_2O$) is liquid at room temperature while hydrogen sulfide ($H_2S$) is a gas, despite $H_2S$ having a higher molecular weight. This is due to the presence of strong hydrogen bonding in $H_2O$. Oxygen is highly electronegative, leading to highly polar O-H bonds and allowing hydrogen atoms to form strong intermolecular hydrogen bonds. Sulfur is less electronegative than oxygen, so $H_2S$ does not form hydrogen bonds. Instead, $H_2S$ molecules are held together by weaker dipole-dipole interactions and London dispersion forces. The stronger hydrogen bonds in $H_2O$ require more energy to overcome, resulting in a higher boiling point and thus $H_2O$ being liquid at room temperature.