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1. A kiloton (kt) of TNT is the energy released in the chemical

explosion of 1000 kg of TNT. A kt is equal to approximately 4x10^12

J (Joules). Enrico Fermi famously measured the energy release of

the first fission test at Trinity by dropping a steady stream of

shredded bits of paper as the thermal blast wave reached the

observation site 10 miles (~15 km) from the explosion. If the paper

bits were displaced a distance of 1 meter by the blast, what was the

energy released in kt ?

 

Discussion of a solution:

------------------------------

The energy of the blast wave can be estimated from the force of the

air times the displacement of the air. The force is the pressure

times the area, which is half of a sphere, or 2*pi*R^2. We can take

the pressure to be atmospheric pressure, or 10^5 N/m^2. This is an

overestimate, but on the other hand the thermal blast energy is an

underestimate of the total energy released which includes gamma rays,

heat, and other physical effects.

 

For R=15 km, we get an energy of Q = Patm x 2 x pi x R^2 x dR x kt/

J, or

 

Q = [10^5 N/m^2] x [2 * 3.14 * (15 x 10^3)^2 m^2] x [ 1 m] x [ 1

kt / 4x10^12 Joules] ~ 35 kt.

 

The Trinity test was more like 20 kt. The displacement Fermi

measured was probably less than 1 meter.

 

A. 0.1 kt

B. 1 kt

C. 30 kt <------------------ answer

D. 1000 kt

E. 3000 kt

 

This event is depicted in the film "Infinity" directed by and

starring Matthew Broderick. This film is a love story and an

excellent depiction of the early life of Richard Feynman.

 

 

 

2. From kt to Mt ("from kilotons to megatons"). The fission blasts

at Trinity, Hiroshima and Nagasaki derived their energy from the mass

difference between uranium (U) or plutonium (Pu) and their fission

products (typically barium and strontium). The binding energy

difference is about 1 MeV per nucleon and U and Pu have about 240

nucleons. (Google "binding energy curve or see Wikipedia.)

Therefore, the energy release is about 240 MeV per fission, and since

1 MeV ~ 2x10^(-13) J, the energy release from 1 kg (~4 moles) of U or

Pu is approximately 20 kt.

 

A fusion blast derives from the mass difference of the hydrogen

isotopes tritium (t) and deuterium (d) and their fusion product He-4

which is about 5 MeV per nucleon per fusion. What is the energy

release from 10 kg of a d-t mixture ?

 

Discussion of a solution:

------------------------------

The d-t reaction results in He-4 nucleus plus a neutron and an energy

release of 5 MeV per nucleon, or about 25 MeV. A mole of d-t mixture

is 5 grams (just the atomic weight in gram units) and there are

6x10^23 nuclei in a mole. The total energy release is a long

multiplication:

 

Q = [10 kg] x [6x10^23 nuclei/mole] x [1 mole/5x10^-3 kg] x [25

MeV/nucleus] x [1.6x10^-13 J/MeV] x [1 kt / 4x10^12 J] = 1 Mt

 

A. 0.001 Mt (1 kt)

B. 0.01 Mt

C. 0.1 Mt

D. 1 Mt <---------------------- answer

E. 100 Mt

 

 

 

3. The nuclear arsenal is "degrading" because tritium has a half-life

of only 12.3 years. The deuterium and tritium is stored in lithium-

hydride (LiH) form as a lithium-tritide-deuteride mixture. If a 3

Mt weapon is built, what is its approximate blast capacity after 25

years ?

 

Discussion of a solution:

------------------------------

In the simplest sense, the tritium decays with a half-life of 12.3

years and, without replenishment, one-half (1/2) is decayed in the

first 12.3 years, and half of that in the next 12.3 years, so only

one-quarter (1/4) is left after 25 years, so the maximum blast is 3

Mt x (1/4) = 0.75 Mt.

 

A. 6 Mt

B. 3 Mt

C. 1.5 Mt

D. 0.75 Mt <-------------------- answer

E. 0.10 Mt

 

 

 

4. Many argue that a new weapon has to be tested to ensure that it

will function as expected. The complexity of a fusion weapon has

been compared to a particle accelerator such as the one at the Pohong

Accelerator Laboratory (PAL), an accelerator/storage ring/beam lines

complex near Daegu consisting of hundreds of precision elements that

define the necessary electric and magnetic fields. If the

reliability of each of 100 components is 99.9% at any one time, what

is the probability that the weapon or accelerator will function when

required?

 

Discussion of a solution:

------------------------------

A reliability of 99.9% can mean that the probability of failure of

one component is 0.001 at any one time. The probability that any one

of a 100 components fails is Pfail = 100 x 0.001 = 0.10. The

probability that all components function is 1 - Pfail = 0.90.

A more direct calculation is to raise the probability to function,

0.999, to the 100th power, since all must function simultaneously.

This gives 0.905 (using a calculator). We used the elementary

notions of probability: if the probabilities of two independent

events are A and B, then the probability of both is A*B, and the

probability of either one is A+B.

 

 

A. 100 %

B. 90 % <-------------------- answer

C. 50 %

D. 1 %

E. 0 %

 

 

 

5. The geopolitical landscape of nine nuclear nations plus one or

two ascending nuclear states is troubling to almost everyone.

What should Ban Ki-moon, Secretary-General of the United Nations, do?

 

Discussion of answer:

---------------------------

The Nuclear Non-Proliferation Treaty that was signed by almost all

nations requires that nations seek the abolition of all nuclear

weapons. This is official US policy, for example, but a very

difficult goal for most political leaders to achieve. Given the

constant pressure for a nation to seek nuclear weapons for whatever

purpose (for deterrence, national pride, future conquest, etc.) and

recognizing that this pressure will never go away, the only safe

number left is zero. Surprisingly, after achieving zero, it is

relatively easy to maintain zero due to the technical capabilities of

the IAEA (International Atomic Energy Agency, Vienna).

 

A. Try to get nations to get along with each other.

B. Prohibit fusion weapons but allow fission weapons.

C. Allow only the US and Russia to have nuclear weapons.

D. Strive to bring nuclear weapons down to zero for

everyone. <------------------------ answer

E. History has shown that we are safe, so "leave well enough alone".