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Chapter 26: Problem 34

An electron has momentum of magnitude $2.4 \times 10^{-22} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s} .$ What is the electron's speed?

Short Answer

Expert verified
Answer: The electron's speed is approximately \(2.63 \times 10^8 \mathrm{m} / \mathrm{s}\).

Step by step solution

01

Write down the given value and constants.

Here, we have the momentum value (\(p = 2.4 \times 10^{-22} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}\)) and the mass of an electron (m_e = \(9.11 \times 10^{-31} \mathrm{kg}\)).
02

Write down the momentum formula.

The formula for momentum is p = mv, where p is momentum, m is mass, and v is velocity.
03

Rearrange the formula to find the velocity.

We can rearrange the momentum formula to isolate the velocity (v). Divide both sides by mass (m): v = p / m
04

Substitute the given values and constants into the formula.

Now, substitute the given values and constants into the formula: v = (2.4 \times 10^{-22} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}) / (9.11 \times 10^{-31} \mathrm{kg})
05

Calculate the velocity.

Perform the calculation: v = (2.4 \times 10^{-22}) / (9.11 \times 10^{-31}) v = 2.63 \times 10^8 \mathrm{m} / \mathrm{s}
06

Final answer.

The electron's speed is approximately \(2.63 \times 10^8 \mathrm{m} / \mathrm{s}\).

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Most popular questions from this chapter

Octavio, traveling at a speed of \(0.60 c,\) passes Tracy and her barn. Tracy, who is at rest with respect to her barn, says that the barn is 16 m long in the direction in which Octavio is traveling, \(4.5 \mathrm{m}\) high, and $12 \mathrm{m}$ deep. (a) What does Tracy say is the volume of her barn? (b) What volume does Octavio measure?
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