Holooly Plus Logo
Holooly Plus Logo

Question 5.11: We found in the last example that if an electron is confined...

We found in the last example that if an electron is confined within the size of a nuclear radius, the uncertainty principle suggests that the minimum kinetic energy of the electron must have a minimum value of about 16 MeV. What does this indicate about the possibility of electrons existing within the nucleus?

The "Step-by-Step Explanation" refers to a detailed and sequential breakdown of the solution or reasoning behind the answer. This comprehensive explanation walks through each step of the answer, offering you clarity and understanding.
Our explanations are based on the best information we have, but they may not always be right or fit every situation.
The Blue Check Mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

This Question has been Answered.

Subscribe

Already have an account?

Login

Related Answered Questions

X rays scattered from rock salt (NaCl) are observed to have an intense maximum at an angle of 20° from the incident direction. Assuming n = 1 (from the intensity), what must be the wavelength of the incident radiation? Strategy We will use Equation (5.1) to find λ, but we need to know d, the

Verified Answer:
In Section 4.1 we showed that   \frac{...

Calculate the de Broglie wavelength of (a) a tennis ball of mass 57 g traveling 25 m/s (about 56 mph) and (b) an electron with kinetic energy 50 eV. Strategy The calculation for both of these wavelengths is a straightforward application of Equation (5.2).

Verified Answer:
(a) For the tennis ball, m = 0.057 kg, so   [...

Determine the de Broglie wavelength for a 54-eV electron used by Davisson and Germer. Strategy We shall use the de Broglie wavelength Equation (5.2) to determine the wavelength λ. We need to find the momentum of a 54-eV electron, but because the energy is so low, we can do a nonrelativistic

Verified Answer:
We write the kinetic energy K.E. in terms of the f...

In introductory physics, we learned that a particle (ideal gas) in thermal equilibrium with its surroundings has a kinetic energy of 3kT/2. Calculate the de Broglie wavelength for (a) a neutron at room temperature (300 K) and (b) a “cold” neutron at 77 K (liquid nitrogen). Strategy In both of these

Verified Answer:
We begin by finding the de Broglie wavelength of t...

We just saw that the speed of a nonrelativistic particle of mass m is not equal to its phase velocity. Show that the particle speed is equal to the group velocity. Strategy We can use the relation for the group velocity in Equation (5.28) or (5.31). Either should work, and using both equations will

Verified Answer:
First, we look at Equation (5.31) for our nonrelat...

Newton showed that deep-water waves have a phase velocity of √gλ/2π. Find the group velocity of such waves and discuss the motion. Strategy We use Equation (5.33) to relate the group and phase velocities, but first we need to find the phase velocity vph in terms of k.

Verified Answer:
If we use \lambda=2 \pi / k, we hav...

In the experiment by Jönsson, 50-keV electrons impinged on slits of width 500 nm separated by a distance of 2000 nm. The observation screen was located 350 mm beyond the slits. What was the distance between the first two maxima? Strategy The equation specifying the orders of maxima and the angle θ

Verified Answer:
We have already calculated the wavelength for elec...

Calculate the momentum uncertainty of (a) a tennis ball constrained to be in a fence enclosure of length 35 m surrounding the court and (b) an electron within the smallest diameter of a hydrogen atom. Strategy We will use Equation (5.40) to find Δpx. The position uncertainty Δx is approximately

Verified Answer:
(a) If we insert the uncertainty of the location o...

Treat the hydrogen atom as a one-dimensional entity of length 2a0 and determine the electron’s minimum kinetic energy. Strategy We will use the uncertainty principle to determine Kmin. Equation (5.43) gives us the minimum kinetic energy for a particle known to be located within a distance l.

Verified Answer:
Equation (5.43) gives   \begin{aligned...

Calculate the minimum kinetic energy of an electron that is localized within a typical nuclear radius of 6 × 10^-15 m. Strategy Let’s assume the minimum electron momentum is equal to that determined by the uncertainty principle for an electron constrained within the distance Δx equal to the nuclear

Verified Answer:
Given that \Delta x \approx r=6 \times 10^{...