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Chapter 2: Q85E (page 67)

An electron accelerated from rest through a potential difference V acquires a speed of 0.9998c. Find the value of V.

Short Answer

Expert verified

The potential energy required to acquire a speed of 0.9998c is25 Mega Volts.

Step by step solution

01

Define relation between kinetic energy and potential difference

The relativistic kinetic energy of a charged particle is equal magnitude to the change in potential energy as it is accelerated through a potential difference.

KE = ΔUKE = qΔV(γ − 1)mec2 = eΔV ...........(1)

02

Determine the potential difference applied

Here,

  • Lorentz factor


    γ=11-u2c2=11-0.9998c2c2=50
  • Mass of electron me = 9.1 × 10−31 kg
  • Charge of electron e = 1.6 × 10−19 C

Putting these values in above equation we get,

localid="1659084824833" (50 − 1) × 9.1 × 10−31 kg × (3 × 108 ms)2 = (1.6 × 10−19) × ΔVΔV = 25.08 MV

So, to get an electron accelerated to a speed of 0.9998c, the required potential difference to be applied is 25 mega volts.

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Most popular questions from this chapter

Suppose particles begin moving in one dimension away from the origin att=0with the following velocities: 0,±1,±2,±3 m/sand so on. (a) After 1 s , how will the velocities of the particles depend on distance from the origin? (b) Now consider an observer on one of the moving particles not at the origin. How will the relative velocities of the other particles depend on distance from the observer?

An object of mass 3mo moves to the right at 0.8c.

a) Calculate its momentum and energy.

b) Using the relativistic velocity transformation, determine its velocity in a new frame of reference moving it to right at 0.5c, then using it to determine the object's momentum and energy in this new frame.

c) Verify that equations role="math" localid="1657556434416" (2-38) are satisfied.

The boron-14nucleus (mass: 14.02266 u) "beta decays," spontaneously becoming an electron (mass: 0.00055 u) and a carbon- 14nucleus (mass: 13.99995 u). What will be the speeds and kinetic energies of the carbon-14nucleus and the electron? (Note: A neutrino is also produced. We consider the case in which its momentum and energy are negligible. Also, because the carbon-14 nucleus is much more massive than the electron it recoils ''slowly'';∴γC≅1 .)

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From a standstill. you begin jogging at5m/s directly toward the galaxy Centaurus A. which is on the horizon 2×1023maway.

(a) There is a clock in Centaurus A. According to you. How Will readings on this clock differ before and after you begin jogging? (Remember: You change
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(b) The planet Neptune is between Earth and Centaurus 4.5×109mis from Earth- How much readings a clock there differ?

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