(d) An a particle is confined in a 'Dy nucleus. Assuming the speed of the a particle is non-relativistic, what is the uncertainty, Av, in the speed of the a particle? (e) If the actual speed, v , of the a particle inside the nucleus is the same as Av, calculate its kinetic energy in MeV. (f) Work out the Coulomb potential energy, in MeV, of the a par- ticle in the electric field of the 50Gd nucleus when it just at the edge of the Gd nucleus. [Assume that the Gd nucleus is the same size as the Dy nucleus, and that the dimensions of the a particle are negligible.] 66-
(d) An a particle is confined in a 'Dy nucleus. Assuming the speed of the a particle is non-relativistic, what is the uncertainty, Av, in the speed of the a particle? (e) If the actual speed, v , of the a particle inside the nucleus is the same as Av, calculate its kinetic energy in MeV. (f) Work out the Coulomb potential energy, in MeV, of the a par- ticle in the electric field of the 50Gd nucleus when it just at the edge of the Gd nucleus. [Assume that the Gd nucleus is the same size as the Dy nucleus, and that the dimensions of the a particle are negligible.] 66-
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Help with d e and f
![(a) The atomic mass of the hydrogen isotope H is 1.007825 amu
(atomic mass unit) and the mass of the neutron is 1.008665 amu,
where 1 amu equals 1.660539 × 10-27 kg. Calculate the binding
energy per nucleon in MeV for the nucleus of the isotope Dy,
which has an atomic mass of 153.924429 amu.
(b) Show that the Dy nucleus is unstable against a decay to
15°Gd, where the atomic mass of l5°Gd is 149.918662 amu
(c) Determine the radius of the l5Dy nucleus.
66
(d) An a particle is confined in a 'Dy nucleus. Assuming the speed
of the a particle is non-relativistic, what is the uncertainty, Av,
in the speed of the a particle?
(e) If the actual speed, v, of the a particle inside the nucleus is the
same as Av, calculate its kinetic energy in MeV.
(f) Work out the Coulomb potential energy, in MeV, of the a par-
ticle in the electric field of the Gd nucleus when it just at the
edge of the Gd nucleus. [Assume that the 5Gd nucleus is the
same size as the Dy nucleus, and that the dimensions of the
a particle are negligible.]
(g) By how much does the kinetic energy of the a particle in (e) fall
short of breaking away from the Gd nucleus?
(h) How can the decay still occur?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fca6289-56d0-42a9-91aa-dda6f4661576%2Fa91a9a36-f9ad-40da-ac81-2d322dc3da71%2Fil0fyg_processed.png&w=3840&q=75)
Transcribed Image Text:(a) The atomic mass of the hydrogen isotope H is 1.007825 amu
(atomic mass unit) and the mass of the neutron is 1.008665 amu,
where 1 amu equals 1.660539 × 10-27 kg. Calculate the binding
energy per nucleon in MeV for the nucleus of the isotope Dy,
which has an atomic mass of 153.924429 amu.
(b) Show that the Dy nucleus is unstable against a decay to
15°Gd, where the atomic mass of l5°Gd is 149.918662 amu
(c) Determine the radius of the l5Dy nucleus.
66
(d) An a particle is confined in a 'Dy nucleus. Assuming the speed
of the a particle is non-relativistic, what is the uncertainty, Av,
in the speed of the a particle?
(e) If the actual speed, v, of the a particle inside the nucleus is the
same as Av, calculate its kinetic energy in MeV.
(f) Work out the Coulomb potential energy, in MeV, of the a par-
ticle in the electric field of the Gd nucleus when it just at the
edge of the Gd nucleus. [Assume that the 5Gd nucleus is the
same size as the Dy nucleus, and that the dimensions of the
a particle are negligible.]
(g) By how much does the kinetic energy of the a particle in (e) fall
short of breaking away from the Gd nucleus?
(h) How can the decay still occur?
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