EXERCISES

Explain, giving reasons, the following sets of quantum numbers are not possible.
$\mathrm{n}=1, \mathrm{l}=1, {\mathrm{m}}_{\mathrm{l}}=0, {\mathrm{m}}_{\mathrm{s}}=+1/2$

Explain, giving reasons, the following set of quantum numbers are not possible.
$\mathrm{n}=3, \mathrm{l}=3, {\mathrm{m}}_{\mathrm{l}}=–3, {\mathrm{m}}_{\mathrm{s}}=+1/2$

Explain, giving reasons, the following set of quantum numbers are possible.
$\mathrm{n}=3, \mathrm{l}=1, {\mathrm{m}}_{\mathrm{l}}=0, {\mathrm{m}}_{\mathrm{s}}=+1/2$

Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.

The longest wavelength doublet absorption transition is observed at $589$ and $589.6 \mathrm{nm}.$ Calculate the frequency of each transition and energy difference between two excited states.

Following results are observed when sodium metal is irradiated with different wavelengths. Calculate (a) threshold wavelength and, (b) Planck's constant.

Similar to electron diffraction, neutron diffraction microscope is also used for the determination of the structure of molecules. If the wavelength used here is 800 pm, calculate the characteristic velocity associated with the neutron.

(a) How many subshells are associated with$\mathrm{n}=4$ ? (b) How many electrons will be present in the subshells having ${\mathrm{m}}_{\mathrm{s}}$ value of $-1/2$ for $\mathrm{n}=4$ ?