Can Two Nuclei with Different Protons and Neutrons Share the Same Nuclear Radii?

[jdp523]

Hey guys,

Really confused by these problems, if anyone can answer them I will email you a coupon for a free medium 2 topping pizza from pizza hut.

1. Is it possible that two nuclei have different number of proton and different number of neutrons, but they have same nuclear radii?

2. Explain why it is important to have neutrons in a multi-particle nucleus.

3. An α particle and a β particle deflects in opposite directions in a uniform magnetic field. If both particles travel with same speed, which will show more deflection?

4. A certain chlorine isotope has its nuclear radius as 4 x 10^-15 m. Find out the number of neutrons in this isotope.

5. Find the daughter nucleus when 226/88Ra undergoes α decay.

6. Find the daughter nucleus when 234/90 Th undergoes β- decay.

7. A 14/7 N nucleus in excited state emits a γ ray with wavelength = 6 x 10^-12 m. Find the resulting decrease in mass of 14/7 N nucleus in this process.

8. A radioactive sample is placed in closed container. 2 days later only 1/4th of the sample is still radioactive. What is the half-life of this sample?

9. The bones of a tiger found to have a C-14 content that is only 15% of what would be found in a similar living animal. How old are these bones? (decay rate λ of C-14 = 3.83 x 10^-12 /sec)

10. Calculate the binding energy of α particle.

11. Complete the following reaction and find the energy it releases:

1/0 n + 235/92 U 140/54 Xe + ………. + 2 (1/0 n)

What type of reaction is this?

 

[RoyalCat]

Oh man, I just got to say I found your incentive outright hilarious!
Welcome to PF. :) I suggest you go over the rules and that you use the formula for posting coursework questions.

What equations do you think are relevant, and what did you try and do until you got stuck?

We're not here to do your homework for you, but to help you understand where you're going wrong and how you can understand the problem.

 

[Fightfish]

1. Yes, radius of the nuclei is dependent on the number of nucleons present.

2. In the nuclei, there are electrostatic forces of repulsion between the protons, and hence neutrons are required to stabilise the nucleus for their ability to form the strong nuclear force without contributing to electrostatic repulsion.

3. β particle. It has a lower mass.

4. R is approximately equal to 1.2 X 10^-15 X A^(1/3)
Hence, we have A = 37 = no of protons + neutrons. Thus no of neutrons = 37-17=20

5. 222/86 Rn
6. 234/91 Pa

7. Energy lost = hc/λ = 3.315 X 10^-14 J = delta M c^2
=> loss in mass = 3.68 X 10^-31 kg

8. 2 days = 2 half-lives => half-life = 1 day

9. e^(-λt) = 0.15 => t = - ln(0.15) / λ = 4.95*10^11 sec = 15700 years

10. Mass defect * c^2. (mass defect = sum of masses of constituent particles - mass of composite particle)

11. I presume there's a missing arrow there.
1/0 n + 235/92 U -> 140/54 Xe + 94/38 Sr + 2 (1/0 n)
Fission.

 

[kuruman]

Fightfish, enjoy your free pizza, but giving out all the answers in less than half an hour from posting does not really help jdp523 learn how to get answers to similar questions on his/her own.

 

[Fightfish]

Sorry about that :(
Have no intention of getting that free pizza whatsoever; we probably don't even live in the same country.