K A Tsokos Solutions for Chapter: Quantum and Nuclear Physics (HL), Exercise 1: Test yourself

What is the evidence for the existance of energy levels in atoms?

Electron of kinetic energy i) 10.10eV, ii) 12.80eV and iii) 13.25eV collide with hydrogen atoms and can excite these to higher states, In each case, find the largest n corresponding to the state the atom can be excited to. Assume that the hydrogen atoms are in their ground state initially.

Theoretically it is possible in principle to balance a pencil on its tip so that it stands vertically on a horizontal table. Explain why in quantum theory this is impossible in principle. (You can turn this problem into a good theoretical extended if essay you try to estimate the time the pencil will stay up after it has been momentarily balanced!)

The graphs represent the wave functions of two electrons. Identify the electron with the least uncertainty in momentum.

The graphs represent the wave functions of two electrons. Identify the electron with the least uncertainty in the position.

Assume that an electron can exist within a nucleus $(size {10}^{-15 }m)$ such that its associated waveforms a fundamental mode standing wave with nodes at the edges of the nucleus. Estimate the wavelength of this electron.

Assume that an electron can exist within a nucleus such that its associated waveforms a fundamental mode standing wave with nodes at the edges of the nucleus. Calculate the kinetic energy of the electron.

Assume that an electron can exist within a nucleus such that its associated waveforms a fundamental mode standing wave with nodes at the edges of the nucleus. And the kinetic energy value is $1.5\times {10}^{-9} J$. Using it comment on whether the electron emitted in beta-minus decay could have existed within the nucleus before the decay.