When an electron makes a transition from its first quantum level to ground level, the energy difference is carried by the emitted photon. In comparison, how much energy is needed to return an electron at ground level to the first quantum level?

Consider photons incident on a hydrogen atom. (a) A transition from the n = 4 to the n = 7 excited-state requires the absorption of a photon of what minimum energy? eV(b) A transition from the n = 1 ground state to the n = 6 excited state requires the absorption of a photon of what minimum energy?  eV

A particle is in the n = 9 excited state of a quantum simple harmonic oscillator well. A photon with a frequency of 3.95 x 1015 Hz is emitted as the particle moves to the n = 7 excited state. What is the minimum photon frequency required for this particle to make a quantum jump from the ground state of this well to the n = 8 excited state? (Give your answer in Hz.)

A photon with wavelength 0.1100 nm collides with a free electron that is initially at rest. After the collision the wavelength is 0.1132 nm. (a) What is the kinetic energy of the electron after the collision? What is its speed? (b) If the electron is suddenly stopped (for example, in a solid target), all of its kinetic energy is used to create a photon. What is the wavelength of this photon?