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Chapter 4: Q47E (page 137)

An electron in an atom can "jump down" from a higher energy level to a lower one, then to a lower one still. The energy the atom thus loses at each jump goes to a photon. Typically, an electron might occupy a level for a nanosecond. What uncertainty in the electron's energy does this imply?

Short Answer

Expert verified

The uncertainty in the electron鈥檚 energy is 鈭�E鈮�5.3脳10-23J.

Step by step solution

01

Given data

Time is given as: 鈭�t=10-9s.

02

Uncertainty principle

The principle states that the position and the velocity of an object cannot be measured with 100 % accuracy at the same time.

鈭�x路鈭�p鈮�h2

鈭�x= Uncertainty in the position.

鈭�p = Uncertainty of momentum.

h = Planck's constant. = 1.05x10-34 J.s

03

Electron’s energy

The Energy and Time Uncertainty Principle,

鈭�t路鈭�E鈮�h2

Substituting values, and we get:

role="math" localid="1658386938701" 鈭�E鈮�1.05脳10-342脳1脳10-9鈭�E鈮�5.3脳10-26J

Therefore, the total energy is 鈭�E鈮�5.3脳10-26J.

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Most popular questions from this chapter

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