Chapter 4: Q43E (page 137)

The position of a neutron in a nucleus is known within an uncertainty of -5x10^-13 m. At what speeds might we expect to find it moving?

Short Answer

Expert verified

The neutron moves at a speed of $∆ v \geq 6.3 \times 10^{6} \frac{m}{s}$ .

Step by step solution

Given data.

Mass of the neutron, m_n= 1.67x10^-27 kg .

Uncertainty in position, $∆ x = 5.0 \times 10^{- 15} m$ .

$h = 1.0545 \times 10^{- 34} J \times s$ .

$∆ v$ = ?

Heisenberg uncertainty principle.

The following equation describes the Heisenberg uncertainty principle for momentum.

$∆ p ∆ x \geq \frac{h}{2} (1)$

Equation for momentum.

The equation for momentum is as follows:

p = m v

By relating above equation with equation (1), then the following relationship will be:

$\begin{array}{rcl} ∆ p ∆ x & \geq & \frac{h}{2} \\ m ∆ v ∆ x & \geq & \frac{h}{2} \end{array}$

Expression for uncertainty in velocity.

The expression for uncertainty in velocity is,

$\begin{array}{rcl} m ∆ v ∆ x & \geq & \frac{h}{2} \\ ∆ v & \geq & \frac{h}{2 m ∆ x} \end{array}$

Estimation of velocity of neutron.

We can estimate the velocity of neutron by solving for $∆ v$

$\begin{array}{rcl} ∆ v & \geq & \frac{h}{2 m ∆ x} \\ \geq & \frac{1.0545 \times 10^{- 34}}{2 \times (1.67 \times 10^{- 27}) \times (5 \times 10^{- 15})} \\ \geq & 6.3 \times 10^{6} \frac{m}{s} \end{array}$

Thus, the neutron moves at a speed of $\begin{array}{rcl} ∆ v & \geq & 6.3 \times 10^{6} \frac{m}{s} \end{array}$ .

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The position of a neutron in a nucleus is known within an uncertainty of -5x10^-13 m. At what speeds might we expect to find it moving?

Short Answer

Step by step solution

Given data.

Heisenberg uncertainty principle.

Equation for momentum.

Expression for uncertainty in velocity.

Estimation of velocity of neutron.

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The position of a neutron in a nucleus is known within an uncertainty of -5x10-13 m. At what speeds might we expect to find it moving?

Short Answer

Step by step solution

Given data.

Heisenberg uncertainty principle.

Equation for momentum.

Expression for uncertainty in velocity.

Estimation of velocity of neutron.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Thermodynamics

Wave Optics

Measurements

Translational Dynamics

Electrostatics

Force

Study anywhere. Anytime. Across all devices.

The position of a neutron in a nucleus is known within an uncertainty of -5x10^-13 m. At what speeds might we expect to find it moving?