2Imagine that you can model an atomic nucleus as a 1-dimensional box for protons

Question

2Imagine that you can model an atomic nucleus as a 1-dimensional box for protons and neutrons whose length is equal to the diameter of the nucleus. If you do an experiment to measure the energy of a neutron in iodine, what is the smallest possible result? Express your answer in eV. (The diameter of an iodine nucleus is12.1 fm. a. Suppose you measure the energy of a neutron in this atom and discover it is in the n-5 energy state. What is the energy that you measured? Express your answer in MeV. b. Once you determine that the wavefunction of the neutron is the n-5,you then proceed to measure the position of the neutron. What is the probability that you will find the neutron within the region 1.21 fm to either side of the center of the nucleus?

Explanation / Answer

2. assuming atomic nucleus as 1d box of length l = 12.1*10^-15 m

so dx = l

and hence form heisenberg's uncertianity principle

dx*dp = h/4*pi

dp = 6.63*10^-34/4*pi*12.1*10^-15

dp = 4.360319*10^-21

so the minimum energy cvan be E = dp^2/2m where m is mass of neutrton

Emin = 5.9413*10^-15 J = 37133.563 eV

a. given the neutron is in n = 5 energy state

now, wavelength of this neutron = lambda

lamdba = 2L/n

and p = h/lambda = nh/2L

hence

En = p^2/2m = n^2h^2/8L^2*m

for n = 5

En = 5.863*10^-12 J = 36.64 MeV

b. As the neutron is always confined inside the box (1 D in this case) the wavefunciton will take a form that has 0 value outosde this box

hence probability of finding the neutron around 1.21 fm of nucleus = 0

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.