An electromagnetic calorimeter made of Pb that has inside a Co-60 source with the activity 4 Ci.The two gamma rays emmited have the energies 1.173 MeV and 1.332 MeV. Calculate the time after that the temperature of the calorimeter rises with T=10 K. C=92J/K (for Pb)
To calculate the time after which the temperature of the calorimeter rises by T=10 K, we need to determine the energy absorbed by the calorimeter from the Co-60 source.
First, we need to calculate the total energy emitted by the Co-60 source. The two gamma rays emitted have energies of 1.173 MeV and 1.332 MeV. To calculate the total energy, we sum up their energies:
Total Energy emitted = Energy1 + Energy2
Total Energy emitted = 1.173 MeV + 1.332 MeV
Now, we need to convert the total energy emitted into joules (J), as the heat capacity (C) of the calorimeter is given in joules per Kelvin (J/K). To convert MeV to joules, we use the conversion factor: 1 MeV = 1.6 x 10^-13 J.
Total Energy emitted (in J) = (1.173 MeV + 1.332 MeV) * (1.6 x 10^-13 J/MeV)
Next, we need to determine the activity of the Co-60 source in Becquerel (Bq). Activity is defined as the number of radioactive decays per second. The activity of a radioactive source can be calculated using the formula:
Activity (in Bq) = Decay constant * Number of radioactive atoms
Decay constant for Co-60 = 0.693 / half-life
The half-life of Co-60 is 5.27 years (or 1.66 x 10^8 seconds). Plugging in these values, we can calculate the decay constant:
Decay constant = 0.693 / (1.66 x 10^8 s)
Given that the activity of the Co-60 source is 4 Ci, we can convert it to Becquerel (Bq) using the conversion factor: 1 Ci = 3.7 x 10^10 Bq.
Activity (in Bq) = 4 Ci * (3.7 x 10^10 Bq/Ci)
Now, we can calculate the rate of energy absorbed by the calorimeter using the formula:
Rate of Energy Absorbed = Activity * Energy emitted
Rate of Energy Absorbed (in J/s) = Activity (in Bq) * Total Energy emitted (in J)
Finally, we can calculate the time (in seconds) it takes for the calorimeter temperature to rise by T=10 K using the formula:
Time = Heat absorbed / (C * Temperature increase)
Time (in seconds) = (Rate of Energy Absorbed) / (C * Temperature increase)
Plugging in the values calculated above, we can find the time after which the temperature of the calorimeter rises by T=10 K.