1. The average mass of Potassium in human body is around 140g. The half-life of K-40 is 1.27e9 years. Estimate the average activity (in Becquerel) of K-40 in human body.

The equation representing radioactivity of isotopes is:

Here,

The average natural abundance of 40K is about 0.0117 %, so N for could be obtained as

follows:

2. How many grams of U-235 are there in 1000kg of NATURAL URANIUM?

Natural uranium has an average atomic mass of 238.026 g/mol.

The atomic fraction of U-235 in natural uranium is 0.724%, that is 0.00724.

This is the ratio of the moles of U-235 to natural uranium.

Atomic mass of U-235 is 235.044 g/mol.

Therefore, the number of grams of U-235 in 100 kg natural uranium is:

3. What (a)kinetic energy and (b)speed (as a fraction of 'c') would a proton have if its relativistic mass were 80% greater than its rest mass?----(given Proton rest mass= 938.27 MeV/c^2)

a) The kinetic energy of a high speed particle is given by:

b) The relativistic mass, is related to the rest mass by:

Where is the Lorentz factor.

The speed of light is our conversion factor between mass and energy. Thus,

So,

It means the total energy of the particle, is in terms of its relativistic mass.

When

Therefore,

4. There is 57.0 mCi  Cs-137 in a reactor. When the source was new it had an activity of 100.0 mCi. What was the date in which the radioactive source was bought?

We know,

From the relationship of radioactive disintegration,

So, the equation may also be written as

Cs-137 has a half-life of about 30 years. Thus,

Therefore, the sample was bought 24 years 4 months ago.

5. The isotope I-132 decays to Xe-132 with a half-life of 2.3 hours.

(a) How long for 7/8 I-132 to decay?

Here,

(b) How long for I-132 to lose 95% of activity?

6. Assume we have to replace the exit Tritium signs of a building after their glow has reached 30% of their original glow. (Given tritium's half-life=12.32 years)

(a) If the glow is proportional to activity, how long (in Years) before they have to replace their

signs?

(b) How much money (in Dollars) in electricity per sign would have been during that time, if an equivalent sign with incandescent bulbs consumes 40W (assume 1kW costs 10cents)

Electricity bill in that time for an equivalent sign with incandescent lamps