Question

What will be the energy in Joules, when an electron acquires a
speed of 10 m/s?

(Answer with solution) ​

Answer 1

Answer:

When you are talking about high-speed electrons, we need to determine whether or not we need to consider Special Relativity. The electron speed is v = 10^6 m/s, and the speed of light c = 3.0 X 10^8 m/s. 

 

v/c = 10^6 / 3.0 X 10^8 = 0.0033, which is a small enough speed ratio to not care about relativstic effects. So, we can use the classical formula for kinetic energy, 

 

KE = (1/2) mv^2

 

m = 9.11 X 10^(-31) kg is the mass of an electron.

 

KE = (1/2)(9.11 X 10^(-31) kg)(10^6 m/s)^2 = 4.56 X 10^(-19) J

Answer 2

The energy of an electron is of the same order (is in the same range) as the energy of light. The lines in the spectrum of an element represent changes in the energy of the electrons in the atoms of that element. By studying these spectra, scientists have come to different conclusions about the behavior of electrons in atoms.

1. The energy of an electron depends on its location relative to the nucleus of an atom. The higher the energy of an electron in an atom, the further its most likely location is from the nucleus. Note that we say likely location. Because of the electron's small size and high energy, we are limited in how accurately we can mark its position at any given moment. We can only describe the regions around the atomic nucleus in which the electron can reside.

2. In describing these regions of space, we also recognize that the electron's energy is quantized. What does this statement mean? A property is quantized if it is available only in multiples of a specified amount. If you're pouring soft drink from a can, you can pour as much or as little as you like. However, if you are buying a soft drink from a vending machine, you can only buy a certain amount. You can't buy a half or a third of a can of soda; you can buy just the whole can or several cans. Soft drinks dispensed by the machine are only available in multiples of the set volume or quanta. The dispensing of soft drinks using the machine was thus quantized.

Energy can also be quantized. If you are climbing a ladder, you can only stop on rungs; you cannot stop between them. The energy required to climb a ladder is used in finite amounts to lift your body from one rung to the next. To move up, you need to use enough energy to move your feet to the next higher rung. If the energy available is only enough to move part way up to the next rung, you can't move at all because you can't stop between rungs. So when climbing a ladder, your energy expenditure is quantized. If you walk up a hill instead of a ladder, your energy expenditure is not quantified. You can go straight up the hill or you can zigzag back and forth and climb gradually. You can take big or small steps; there are no limits to where you can stop or how much power you have to use.

When you talk about high-speed electrons, we need to determine whether we need to consider special relativity or not. The speed of an electron is v = $10^{6}$ m/s and the speed of light is c = $3.0 * 10^8$ m/s.

v/c = $(1/2) mv^2$$10^6 / 3.0 * 10^8 = 0.0033$, which is a small enough velocity ratio to not care about relativistic effects. So we can use the classical formula for kinetic energy,

KE = $(1/2) mv^2$

m = $9.11 *10^{-31}$ kg is the mass of an electron.

KE = $(1/2) (9.11 * 10^{-31} kg)(10^6 m/s)^2 = 4.56 *10^{-19}$$)$J

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