HW 2: Bohr Model, Wave-Particle Duality and Uncertainty

Question-1¶

• Sketch derivation of Rydberg’s empirical formula for spectral lines using Bohr’s atomic model.

• Indicate which assumptions are motivated by classical mechanics and which are ad-hoc quantum rules.

Question-2¶

• Why is there a need to use reduced mass instead of just electron mass in Bohr’s formula?

• Compute ionization energy of $Li^{2+}$ and comment on how much using reduced mass $\mu$ changes energy spacings compared to just using electron mass $m_e$

Question-3¶

A ground-state hydrogen atom absorbs a photon of light that has a wavelength of 97.2 nm. It then gives off a photon that has a wavelenth of 486 nm.

• What is the final state of the hydrogen atom?

Question-4¶

If the speed of neutron is given by $v=\Big(\frac{3k_B T}{m_n} \Big)^{1/2}$ where m is the mass of a neturon then what temperature is needed so that the neutrons have a de Broglie wavelength of 50 pm?

Question-5¶

• What is the uncertainty of the momentum of an electron if we know its position is womehere in a $10^{-12}m$ interval?

• How does the value compare to memontum of an electron in the first Bohr orbit?