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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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