Alpha particle close to the nucleus

AI Thread Summary
The discussion revolves around a discrepancy in calculating the radius of an alpha particle's interaction with a nucleus, where the participant's result differs significantly from the textbook's answer. The participant initially calculated the velocity using kinetic energy but realized their value was slightly higher than expected, leading to confusion. Other contributors confirmed the textbook's solution and pointed out that the velocity calculation was unnecessary, as the kinetic energy can be directly used in the relevant formula. The key takeaway was that the participant's misunderstanding stemmed from not recognizing that the kinetic energy relates directly to the momentum formula. Ultimately, the participant corrected their approach and arrived at the correct solution.
Juli
Messages
24
Reaction score
6
Homework Statement
What is the impact parameter of an alpha particle with kinetic energy 4 MeV that is deflected by the angle ##\theta = 15°## when scattered by a gold nucleus (Z =79)?
Relevant Equations
$$p = \frac{k}{mv_0^2}cot\frac{\theta}{2} $$ with $$k = \frac{2Ze^2}{4\pi\epsilon_0}$$
Hello everyone, while studying I found this task in my textbook.
Solving this problem with the help of the formula seems quite straightforward. But I get a different result than the solution the textbook offers.
I get: Around ##5∗10^{−15}m## (which is a typical solution for a radius of a nucleus)
Textbook says: ##2.16∗10^{−13}m##The point where I think I probably could be mistaken, is the velocity ##v_0##. I calculated it with ##E= \frac{1}{2}m∗v^2## with ##E=4MeV##.
Is that wrong? I get ##v_0=1.44∗10^7\frac{m}{s}## (which I think is already relativistic, so I think there is my mistake?)
Can anyone verify the solution of the textbook?
I would be very grateful for any help, since I'm quite confused.
 
Last edited:
Physics news on Phys.org
A kinetic energy of 4 Mev is nonrelativistic for an alpha particle, which has a rest mass energy of about 3.7 Gev. For the speed of the alpha particle, I get 1.38 x 107 m/s, which is a little less than your value. This is about 5% the speed of light.

Your formula looks correct. I get the textbook's answer for the impact parameter. The only way we can identify your mistake is for you to show your calculation explicitly with all the numerical values and units for the various quantities.
 
  • Like
Likes berkeman, PeroK and Juli
Juli said:
Can anyone verify the solution of the textbook?
Like @TSny, I get the same answer as the text book.

Your value for ##v_0 (1.44\times 10^7m/s)## is about 4% bigger than the correct value (a small but signficant difference). You might want to sort out why.

In fact there is no need to work out ##v_0##. In the formula ##p = \frac{k}{mv_0^2}cot\frac{\theta}{2}## note that ##mv_0^2## is simply twice the kinetic energy, i.e. ##mv_0^2 = 8MeV##.
 
Thank you both so much.
Steve4Physics said:
Like @TSny, I get the same answer as the text book.

Your value for ##v_0 (1.44\times 10^7m/s)## is about 4% bigger than the correct value (a small but signficant difference). You might want to sort out why.

In fact there is no need to work out ##v_0##. In the formula ##p = \frac{k}{mv_0^2}cot\frac{\theta}{2}## note that ##mv_0^2## is simply twice the kinetic energy, i.e. ##mv_0^2 = 8MeV##.
Especially the point about ##mv^2## was very helpful. There was my mistake, I get the right solution now.
 
  • Like
Likes berkeman and TSny
Thread 'Minimum mass of a block'
Here we know that if block B is going to move up or just be at the verge of moving up ##Mg \sin \theta ## will act downwards and maximum static friction will act downwards ## \mu Mg \cos \theta ## Now what im confused by is how will we know " how quickly" block B reaches its maximum static friction value without any numbers, the suggested solution says that when block A is at its maximum extension, then block B will start to move up but with a certain set of values couldn't block A reach...
TL;DR Summary: Find Electric field due to charges between 2 parallel infinite planes using Gauss law at any point Here's the diagram. We have a uniform p (rho) density of charges between 2 infinite planes in the cartesian coordinates system. I used a cube of thickness a that spans from z=-a/2 to z=a/2 as a Gaussian surface, each side of the cube has area A. I know that the field depends only on z since there is translational invariance in x and y directions because the planes are...
Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'
Figure 1 Overall Structure Diagram Figure 2: Top view of the piston when it is cylindrical A circular opening is created at a height of 5 meters above the water surface. Inside this opening is a sleeve-type piston with a cross-sectional area of 1 square meter. The piston is pulled to the right at a constant speed. The pulling force is(Figure 2): F = ρshg = 1000 × 1 × 5 × 10 = 50,000 N. Figure 3: Modifying the structure to incorporate a fixed internal piston When I modify the piston...
Back
Top