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Yes, it is possible for a photon to not have enough energy. If it does not then it won't be able to eject an electron. Like in lecture on Week 2, a photon packet overall does not need to have intense energy, but each photon itself must have enough intensity.
Yes, there can be cases where the photons do not have enough energy to eject an electron. If there is not enough energy, then the electron will stay in whatever orbital it is currently in and will not jump to the other orbitals.
In response to Jorge's question, if a photon has enough energy within it, it can interact with an electron which is on its path and then displace its position. It can affect its velocity because if the electron is put on a different trajectory, its distance it travels is changed, causing the velocity to change since velocity is a vector for distance/time.
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