Q38E From equations (3-4) to (3-6) ob... [FREE SOLUTION]

Chapter 3: Q38E (page 94)

From equations (3-4) to (3-6) obtain equations (3.8). It is easiest to start by eliminating 蠁 between equations (3-4) and (3-5) using cos²蠁+蝉颈苍²蠁 = 1 The electron speed u may then be eliminated between the remaining equations.

Short Answer

Expert verified

Using the given equations, the following can be obtained is $位' - 位 = \frac{h}{m_{e} c} (1 - \cos 胃)$ .

Step by step solution

Given data

$\frac{h}{位} = \frac{h}{位'} \cos 胃 + 纬_{u} m_{e} u \cos 蠒鈥� . . (1) 0 = \frac{h}{位'} \sin 胃 - 纬_{u} m_{e} u \sin 蠒鈥� . . (2) \frac{h c}{位} - m_{e} c^{2} = \frac{h c}{位'} + 纬_{u} m_{e} c^{2} 鈥� . . (3)$

Concept used

Einstein's mass-energy equivalence relation can be expressed as,

E = mc²

Use the equations and solve

Rearranging the above equations (1 and 2) will give:

$纬_{u} m_{e} u \cos 蠒 = \frac{h}{位} - \frac{h}{位'} \cos 胃纬_{u} m_{e} u \sin 蠒 = \frac{h}{位'} \sin 胃$

Squaring both will give:

${(纬_{u} m_{e} u)}^{2} \cos^{2} 蠒 = {(\frac{h}{位} - \frac{h}{位'} \cos 胃)}^{2} {(纬_{u} m_{e} u)}^{2} \sin^{2} 蠒 = {(\frac{h}{位'} \sin 胃)}^{2}$

Adding both equations will lead to:

${(纬_{u} m_{e} u)}^{2} = {(\frac{h}{位})}^{2} - \frac{2 h^{2}}{位位'} \cos 胃 + {(\frac{h}{位'})}^{2}$ 鈥�..(4)

The Square of equation 3 will give

${(纬_{u} m_{e} u)}^{2} = {(\frac{h}{位})}^{2} + {(\frac{h}{位})}^{2} - \frac{2 h^{2}}{位位'} + 2 m_{e} c (\frac{h}{位} - \frac{h}{位'}) + m_{e}^{2} c^{2}$ 鈥�..(5)

Subtract equation 5 from equation 4

Simplify further,

$\begin{array}{rcl} m_{e}^{2} (纬_{u}^{2} c^{2} - 纬_{u}^{2} c^{2}) & = & - \frac{2 h^{2}}{位位'} (1 - \cos 胃) + 2 m_{e} c (\frac{h}{位'} - \frac{h}{位}) + {(m_{e} c)}^{2} \\ \frac{2 h^{2}}{位位'} (1 - \cos 胃) & = & 2 m_{e} c (\frac{h}{位'} - \frac{h}{位}) \\ \frac{h}{位位'} (1 - \cos 胃) & = & m_{e} c (\frac{1}{位'} - \frac{1}{位}) \\ 位 - 位' & = & \frac{h}{m_{e} c} (1 - \cos 胃) \end{array}$

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91影视

From equations (3-4) to (3-6) obtain equations (3.8). It is easiest to start by eliminating 蠁 between equations (3-4) and (3-5) using cos²蠁+蝉颈苍²蠁 = 1 The electron speed u may then be eliminated between the remaining equations.

Short Answer

Step by step solution

Given data

Concept used

Use the equations and solve

Subtract equation 5 from equation 4

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Most popular questions from this chapter

Recommended explanations on Physics Textbooks

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91影视

From equations (3-4) to (3-6) obtain equations (3.8). It is easiest to start by eliminating 蠁 between equations (3-4) and (3-5) using cos2蠁+蝉颈苍2蠁 = 1 The electron speed u may then be eliminated between the remaining equations.

Short Answer

Step by step solution

Given data

Concept used

Use the equations and solve

Subtract equation 5 from equation 4

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Quantum Physics

Electric Charge Field and Potential

Further Mechanics and Thermal Physics

Space Physics

Magnetism

Mechanics and Materials

Study anywhere. Anytime. Across all devices.

From equations (3-4) to (3-6) obtain equations (3.8). It is easiest to start by eliminating 蠁 between equations (3-4) and (3-5) using cos²蠁+蝉颈苍²蠁 = 1 The electron speed u may then be eliminated between the remaining equations.