Physics for Scientists and Engineers, 6e. Chapter 42 - Atomic Physics. A hydrogen atom is in its ground state. Incident on the atom are many photons each having an energy of 10.5 eV. The result is that. the atom is excited to a higher allowed state the atom is ionized
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Chapter 42 - Atomic Physics
Because the energy of 10.5 eV does not correspond to raising the atom from the ground state to an allowed excited state, there is no interaction between the photon and the atom.
When electrons collide with an atom, they can transfer some or all of their energy to the atom. Suppose a hydrogen atom in its ground state is struck by many electrons each having a kinetic energy of 10.5 eV. The result is that
A hydrogen atom makes a transition from the n = 3 level to the n = 2 level. It then makes a transition from the n = 2 level to the n = 1 level. Which transition results in emission of the longest-wavelength photon?
As the electrons strike the atom, they can give up any amount of energy between 0 and 10.5 eV, unlike the photons in question 1, which must give up all of their energy in one interaction. Thus, those electrons that undergo the appropriate collision with the atom can transfer 13.606 eV – 3.401 eV = 10.205 eV to the atom and excite it to the n = 2 state. Those electrons that do not make the appropriate collision will transfer only enough kinetic energy to the atom as a whole to satisfy conservation of momentum in the collision, without raising the atom to an excited state.
The longest-wavelength photon is associated with the lowest energy transition, which is n = 3 to n = 2.
The number of subshells is the same as the number of allowed values of ℓ. The allowed values of ℓ for n = 4 are ℓ = 0, 1, 2, and 3, so there are four subshells.
Nine different values (–4, –3, –2, –1, 0, 1, 2, 3, 4) of mℓ, as follows:
In the hydrogen atom, the quantum number n can increase without limit. Because of this, the frequency of possible spectral lines from hydrogen also increases without limit.
If the energy of the hydrogen atom were proportional to n (or any power of n), the energy would become infinite as n grows to infinity. But the energy of the atom is inversely proportional to n2. Thus, as n increases to very large values, the energy of the atom approaches zero from the negative side. As a result, the maximum frequency of emitted radiation approaches a value determined by the difference in energy between zero and the (negative) energy of the ground state.
The higher the value of Z, the closer to zero is the energy associated with the outermost electron and the smaller is the ionization energy.
The wavelengths of the characteristic x-rays are determined by the separation between energy levels in the atoms of the target, which is unrelated to the energy with which electrons are fired at the target. The only dependence is that the incoming electrons must have enough energy to eject an atomic electron from an inner shell.
If the electrons arrive at the target with very low energy, atomic electrons cannot be ejected and characteristic x-rays do not appear. Because the incoming electrons experience accelerations, the continuous spectrum appears.