Example 9 Find the momentum of photon that caused the ionization of the hydrogen atom (kg m/s) Example 10 Find the first excitation potential of singly ionized helium atoms (V) Example 11 The hydrogen atom emitted photon with a wavelength of 486 nm.Find the energy changing of electron (eV)

Example 9:The momentum of a photon can be calculated using the formula: where is the momentum, is Planck's constant ( ), and is the wavelength of the photon.For the ionization of a hydrogen atom, the wavelength of the photon is typically around 121.6 nm (for the Lyman series). Plugging this value into the formula gives: So, the momentum of the photon is approximately .Example 10:The first excitation potential of singly found using the formula: where is the energy, is the atomic number (2 for helium), is the lower energy level (1 for the ground state), and is the higher energy level (2 for the first excitation).For helium, the first excitation potential is: So, the first excitation potential of singly ionized helium atoms is 40.8 eV.Example 11:The energy change of an electron in a hydrogen atom emitting a photon can be calculated using the formula: where is the energy change, is Planck's constant ( ), is the speed of light ( ), and is the wavelength of the photon.For a wavelength of 486 nm (or ), the energy change is: Converting joules to electron volts (1 eV = ): So, the energy change of the electron is approximately 2.56 eV.