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I understand that electrons can possess only discrete amounts of energy so if an electron in an atom has to jump from a lower orbit to a higher orbit it will require a discrete amount of energy to the same. Say for example it requires 2 units of energy to jump to the higher level. So instead supplying that exact 2 units what if I supply a little less say 1.9999999999999... units, will it make the jump? If not does it need to be the exact 2 units?

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Generally speaking you must provide the exact amount of energy needed for the transition from one energy state to another. That is, this is a physical phenomenon that requires a specific amount of energy. However, your question has some subtleties with regard to any practical situation.

  • Depending on your measuring devices, you may not have enough precision to detect a difference between 2 and 1.9999999999999, so it might appear that you could achieve the jump with less energy than required.

  • If you measuring devices are not calibrated correctly, they may not have the proper accuracy so again your measurement might suggest that you could make the jump with less energy.

  • If you are implying a value of 1.9999 with the 9's extending to infinity, than this - mathematically - is indeed equal to the value of 2.

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