Phy 203: General Physics III
Chapter 31 Worksheet
2/6/2016
1
Isotopes & the Atomic Nucleus:
1. Consider an isotope of helium: helium-4.
a. Write the isotope symbol for helium-4.
b. How many nucleons does this isotope have?
c. How many neutrons does this isotope have?
d. Estimate the nuclear radius for helium-4.
e. Estimate the Coulomb force between the protons on helium-4.
f. How does this value compare with the force between the protons and the electrons?
Estimate the force between the helium-4 nucleus and an orbiting electron. The average
Bohr radius for an electron (in the ground state) of an atom is ao/Z, where ao is the Bohr
radius for hydrogen (ao=5.29 x10-11 m) and Z is the atomic number.
2. Consider 2 isotopes of carbon: carbon-12 and carbon-14. The average atomic radius for a
carbon atom is roughly 1.5x10-10 m.
g. Write the isotope symbol for each of these isotopes
h. How many nucleons does each of these isotopes have?
i.
How many neutrons does each isotope have?
j. What is the mass (in kg) of each of these isotopes?
Phy 203: General Physics III
Chapter 31 Worksheet
2/6/2016
2
k. Calculate the nuclear radius for each of these isotopes.
l.
Compare the atomic radius to nuclear radius for carbon-12. Determine the ratio of atomic
radius to nuclear radius.
m. Estimate the volume of the carbon-12 atom and its nucleus. Assume that both are
spheres.
n. Determine both the atomic density and the nuclear density for both carbon-12. How do
they compare?
o. Repeat Parts (f)-(h) for carbon-14.
Phy 203: General Physics III
Chapter 31 Worksheet
2/6/2016
3
Mass Defect and Nuclear Binding Energy:
3. Consider the isotope, helium-4.
a. What is the mass of a proton (in kg)? (in amu)?
b. What is the mass of a neutron (in kg)? (in amu)?
c. Calculate the mass of all of the protons & neutrons in the helium isotope (add up the
masses).
d. The mass of a helium-4 atom is actually 6.6447x10-27 kg. Calculate the mass deficit for
one atom.
e. Calculate the binding energy for a helium-4 atom.
f. Calculate the binding energy for 4.00 grams of this helium-4.
2. 2 isotopes of hydrogen, hydrogen-2 (2.014 amu) and hydrogen-3 (3.016 amu), are combined
in a nuclear fusion process. The product of this process is a helium-4 nucleus and a neutron.
a. Calculate the total mass in kg for the 2 hydrogen isotopes.
b. Calculate the total mass of helium and the neutron in kg.
c. Calculate the mass deficit between the hydrogen isotopes and the helium/neutron
products.
d. Use the mass deficit in (c) to determine the energy gained/released during this process.
e. Is this energy gained or released by this process? Explain your answer.
Phy 203: General Physics III
Chapter 31 Worksheet
2/6/2016
4
Carbon-14 & Isotope Dating
1) A fossil sample has 25% of its original
14
C.
a) How old is the fossil?
b) The fossil has 100 14C atoms when you test it. How many
when the organism died?
c) Estimate how many
d) When
14
12
14
C atoms did the fossil have
C atoms the fossil originally had when it died.
C decays it ejects a beta particle. What is the identity of the decayed atom?
e) Write the equation for the nuclear decay of
2) A fossil sample has 15% of its original
14
14
C.
C.
a) How old is the fossil?
b) The fossil has 15,000 14C atoms when you test it. How many
when the organism died?
c) Estimate how many
12
14
C atoms did the fossil have
C atoms the fossil originally had when it died.
d) What was the rate of carbon-14 decay, N/t, when the fossil died? Now?
3) A certain radio-labeled substance contains 1000 3H atoms. Thirty-five years later, the sample
has 250 3H atoms remaining.
a) What is the half-life of 3H?
b) When 3H decays it ejects a beta particle, write the equation for the nuclear decay of 3H.
4) When uranium-238 decays, it produces a thorium-234.
a) What is the likely radiation type emitted? How can you tell?
b) Write the equation for the nuclear decay.
Phy 203: General Physics III
Chapter 31 Worksheet
2/6/2016
5
5) When lead-214 (214Pb) decays, it produces a bismuth-214 (214Bi).
a) What is the likely radiation type emitted?
b) Write the equation for the nuclear decay of lead-214.
6) Radon-222 (222Ra) is a well-documented health hazard for humans. It naturally occurs as
part of the complicated decay chain of uranium-238 (238U). When radon-222 decays, it produces
a polonium-218. The half-life for 222Ra is 3.83 days.
a) What is the likely radiation type emitted by radon decay?
b) Write the equation for the nuclear decay of radon-222.
c) If a sample of
later?
d) How many
222
222
Ra originally has 5,000 atoms, how many are atoms remain 15.3 days
Ra atoms remain 20 days later?
e) What is rate of decay, N/t, in question (d)?