Chapter 37: Q. 27 (page 1082)

What is the velocity, as a fraction of c, of
a. A proton with 500 GeV total energy?
b. An electron with 2.0 GeV total energy?
Hint: This problem uses relativity.

Short Answer

Expert verified

(a) Velocity of the given proton will be $0.999998 c$ .

(b) Velocity of the given electron will be $0.99999997 c$ .

Step by step solution

Part (a) Step 1 Given Information :

Given that, A proton having total energy 500 GeV .

We need to find it's velocity in the fraction of c.

Part (a) Step 2 Simplification :

Total energy is $E = 500 GeV = 500 \times 10^{9} eV = 500 \times 10^{9} \times 1.6 \times 10^{- 19} J$ .

Mass of the proton is 1.67 × 10^-27 kg.

So if V is the velocity of the proton then we have

$E = \frac{m c^{2}}{\sqrt{1 - v^{2} / c^{2}}}$

$\Rightarrow 500 \times 10^{9} \times 1.6 \times 10^{- 19} = \frac{1.67 \times 10^{- 27} \times {(3 \times 10^{8})}^{2}}{\sqrt{1 - v^{2} / c^{2}}}$

$\Rightarrow V = \pm 0.999998 c$ .

So, The velocity of proton is $0.999998 c$ .

Part (b) Step 1 Given Information:

Given that, An electron having total enegy 2.0 GeV .

We need to find it's velocity in the fraction of c.

Part (b) Step 2 Simplification :

The energy of the electron is

$E = 2.0 GeV = 2.0 \times 10^{9} \times 1.6 \times 10^{- 19} J$ .

And the mass of the electron is $9.10 \times 10^{- 31} k g$ .

Hence we have

$E = \frac{m c^{2}}{\sqrt{1 - v^{2} / c^{2}}}$

$\Rightarrow 2.0 \times 10^{9} \times 1.6 \times 10^{- 19} = \frac{9.2 \times 10^{- 27} \times {(3 \times 20^{8})}^{2}}{\sqrt{1 - v^{2} / c^{2}}}$

$\Rightarrow v = \pm 0.99999997 c$

So the velocity of electron will be $0.99999997 c$ .

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What is the velocity, as a fraction of c, of
a. A proton with 500 GeV total energy?
b. An electron with 2.0 GeV total energy?
Hint: This problem uses relativity.

Short Answer

Step by step solution

Part (a) Step 1 Given Information :

Part (a) Step 2 Simplification :

Part (b) Step 1 Given Information:

Part (b) Step 2 Simplification :

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What is the velocity, as a fraction of c, ofa. A proton with 500 GeV total energy?b. An electron with 2.0 GeV total energy?Hint: This problem uses relativity.

Short Answer

Step by step solution

Part (a) Step 1 Given Information :

Part (a) Step 2 Simplification :

Part (b) Step 1 Given Information:

Part (b) Step 2 Simplification :

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Linear Momentum

Energy Physics

Modern Physics

Circular Motion and Gravitation

Wave Optics

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

What is the velocity, as a fraction of c, of
a. A proton with 500 GeV total energy?
b. An electron with 2.0 GeV total energy?
Hint: This problem uses relativity.