Chapter 38

Find the energy difference between the ground state of hydrogen and deuterium (hydrogen with an extra neutron in the nucleus)

An excited hydrogen atom, whose electron is in an \(n=4\) state, is motionless. When the electron falls into the ground state, does it set the atom in motion? If so, with what speed?

The radius of the \(n=1\) orbit in the hydrogen atom is $$ a_{0}=0.053 \mathrm{nm} $$ a) Compute the radius of the \(n=6\) orbit. How many times larger is this compared to the \(n=1\) radius? b) If an \(n=6\) electron relaxes to an \(n=1\) orbit (ground state), what is the frequency and wavelength of the emitted radiation? What kind of radiation was emitted (visible, infrared, etc.)? c) How would your answer in (a) change if the atom was a singly ionized helium atom \(\left(\mathrm{He}^{+}\right),\) instead?

An electron in a hydrogen atom is in the ground state (1s). Calculate the probability of finding the electron within a Bohr radius \(\left(a_{0}=0.05295 \mathrm{nm}\right)\) of the proton. The ground state wave function for hydrogen is: \(\psi_{1 s}(r)=A_{1 s} e^{-r / a_{0}}=e^{-r / a_{0}} / \sqrt{\pi a_{0}^{3}}\).