Electric field at surface of lead-208 nucleus

In summary, the given conversation discusses the relationship between the volume of a nucleus and the volume of a proton, represented by the respective radii. By equating the two volumes, the expression ## r = (208)^{1/3}(1.20 \times 10^{-15} m)## is obtained, which shows the proportional relationship between the two radii.
  • #1
ChiralSuperfields
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Homework Statement
Please see below
Relevant Equations
Please see below
For this problem,
1674151948824.png

The solution is,
1674151982159.png

However why is ## r = (208)^{1/3}(1.20 \times 10^{-15} m)##

Many thanks!
 
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  • #2
Just write the relationship given, between the volume of proton and volume of nucleus in terms of the respective radius. (##V=208 V_p##).
 
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  • #3
nasu said:
Just write the relationship given, between the volume of proton and volume of nucleus in terms of the respective radius. (##V=208 V_p##).
Thanks for your reply @nasu!

I will use ##r## for the radius of the nucleus and ##R## for the radius of the proton.

## \frac {4{\pi}r^3} {3} = 208\frac {4{\pi}R^3} {3}##
## r =(208R^3)^{1/3}##
## r = 208^{1/3}R ##
## r = (208)^{1/3}(1.20 \times 10^{-15} ## ##m)##

Thank you I see how they got it now!
 
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1. What is the electric field at the surface of a lead-208 nucleus?

The electric field at the surface of a lead-208 nucleus is dependent on the charge and size of the nucleus. It is typically on the order of 10^12 volts per meter.

2. How is the electric field at the surface of a lead-208 nucleus calculated?

The electric field at the surface of a lead-208 nucleus can be calculated using the equation E = kQ/r^2, where E is the electric field, k is the Coulomb constant, Q is the charge of the nucleus, and r is the radius of the nucleus.

3. Why is the electric field at the surface of a lead-208 nucleus important?

The electric field at the surface of a lead-208 nucleus is important because it affects the behavior of charged particles near the nucleus. This can have implications in nuclear reactions and particle interactions.

4. How does the electric field at the surface of a lead-208 nucleus compare to other nuclei?

The electric field at the surface of a lead-208 nucleus is relatively strong compared to other nuclei. This is due to its large size and high charge, which result in a higher electric field strength.

5. Can the electric field at the surface of a lead-208 nucleus be manipulated?

Yes, the electric field at the surface of a lead-208 nucleus can be manipulated by changing the charge or size of the nucleus. This can be done through nuclear reactions or by applying external electric fields.

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