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Determine the energy required to accelerate an electron from (a) 0.500$c$ to 0.900$c$ and (b) 0.900$c$ to 0.990$c .$

a) 0.582$M e V$

b) 2.45 $\mathrm{MeV}$

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Cornell University

Numerade Educator

University of Washington

McMaster University

Let's do part, eh? Well, the change of the energy is Delta key is equal to one divided by square root off one minus. We f divided by see whole square minus one, divided by one divided by, uh squared Ruto one minus one minus. Oh, the initial the initial divided by sea Whole square times e r The rest energy on dhe. Let's plug in the values. Well changing energy is equal to one divided by screed. Route off one minus. We have a cedar 10.900 All scare C squared gets canceled with C square. Since we have zero point, find 00 times the speed of light. Um, minus one divided by our square root off one minus zero point 500 Hold scare. Multiply by, uh, rest in receiving. Concede a 0.511 1,000,000 electron volts 1,000,000 electron balls and solving this change. No, that energy Delta K is equal to 0.5, babe. Two million electron. Walt. All right. Now let's to part B again using, uh, the same week Origen Well, changing energy is a cool too one divided by square root off one minus. Um, we have divided by a C old square minus one, divided by square root off one minus. Ah, oui. I divided by. See? Whole square times. Uh, the rest energy. Now let's split in the values. So, uh, change in energy is equal to, um, one divided by square root off one minus, Uh, 0.90 See the whole square minus one, divided by square. Root off one minus again. We have, uh, see the point. This is zero point. My 92. Excuse me. This is, uh, zero point 990 and one minus. Here we have 0.900 all square multiply by, uh, 0.511 million electron world and therefore change in kinetic changing energy is equal to 2.45 million electrons, 2.45 billion electron volts.