Q. 16 At what speed is an electron's d... [FREE SOLUTION]

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Chapter 38: Q. 16 (page 1114)

At what speed is an electron's de Broglie wavelength (a) $1.0 pm$ , (b) $1.0 nm$ , (c) $1.0 渭 m$ , and (d) $1.0 mm$ ?

Short Answer

Expert verified

(a) $v = 7.27 脳 10^{8} m / s$

(b) $v = 2.77 脳 10^{8} m / s$

(d) $v = 0.727 m / s$

Step by step solution

Part(a) Step 1: Given Information

The electron's de Broglie wave length is $1.0 p m$

Part(a) Step 2: Calculation

We can start the solution with expression for de-Broglie wavelength

$位 = \frac{h}{m v} v = \frac{h}{m 位} v = \frac{6.63 脳 10^{- 34}}{(9.11 脳 10^{- 31}) (1 脳 10^{- 12})} v = 7.27 脳 10^{8} m / s$

This speed is larger than speed of light, so we must calculate relativistic speed:

$位 = \frac{h}{p} p = 纬 m v \frac{h}{位} = 纬 m v 纬 = \frac{1}{\frac{h}{1 - \frac{v^{2}}{c^{2}}}} \frac{h}{位} (1 - \frac{v^{2}}{c^{2}}) = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} m v^{2} \frac{h^{2}}{位^{2}} = v^{2} (m^{2} + \frac{h^{2}}{位^{2} c^{2}}) v = \frac{h}{位路 \sqrt{(m^{2} + \frac{h^{2}}{位^{2} c^{2}})}} v = 2.77 脳 10^{8} m / s$

Part(b) Step 1: Given Information

The electron's de Broglie wave length is $1.0 n m$

Part(b) Step 2: Calculation

For $位 = 1 脳 10^{- 9}$ we have:

$位 = \frac{h}{m v} v = \frac{h}{m 位} v = \frac{6.63 脳 10^{- 34}}{(9.11 脳 10^{- 31}) (1 脳 10^{- 9})} v = 7.27 脳 10^{5} m / s$

Part(c) Step 1: Given Information

The electron's de Broglie wave length is $1.0 渭 m$

Part(c) Step 2: Calculation

For $位 = 1 脳 10^{- 6}$ we have:

$v = \frac{h}{m 位} v = \frac{6.63 脳 10^{- 34}}{(9.11 脳 10^{- 31}) (1 脳 10^{- 6})} v = 7.27 脳 10^{2} m / s$

Part(d) Step 1: Given Information

The electron's de Broglie wave length is $1.0 m m$

Part(d) Step 2: Calculation

For $位 = 1 脳 10^{- 3}$ we have:

$v = \frac{h}{m 位} v = \frac{6.63 脳 10^{- 34}}{(9.11 脳 10^{- 31}) (1 脳 10^{- 3})} v = 0.727 m / s$

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91影视

At what speed is an electron's de Broglie wavelength (a) $1.0 pm$ , (b) $1.0 nm$ , (c) $1.0 渭 m$ , and (d) $1.0 mm$ ?

Short Answer

Step by step solution

Part(a) Step 1: Given Information

Part(a) Step 2: Calculation

Part(b) Step 1: Given Information

Part(b) Step 2: Calculation

Part(c) Step 1: Given Information

Part(c) Step 2: Calculation

Part(d) Step 1: Given Information

Part(d) Step 2: Calculation

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91影视

At what speed is an electron's de Broglie wavelength (a) 1.0pm, (b) 1.0nm, (c) 1.0渭m, and (d)1.0mm ?

Short Answer

Step by step solution

Part(a) Step 1: Given Information

Part(a) Step 2: Calculation

Part(b) Step 1: Given Information

Part(b) Step 2: Calculation

Part(c) Step 1: Given Information

Part(c) Step 2: Calculation

Part(d) Step 1: Given Information

Part(d) Step 2: Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism

Wave Optics

Modern Physics

Fields in Physics

Atoms and Radioactivity

Force

Study anywhere. Anytime. Across all devices.

At what speed is an electron's de Broglie wavelength (a) $1.0 pm$ , (b) $1.0 nm$ , (c) $1.0 渭 m$ , and (d) $1.0 mm$ ?