Pu-238 is radioactive by alpha-decay (half-life 87.7 y). Each decay releases 5.6 MeV of energy. Pu-238 is sometimes used to power space probes. If all the decay energy can be converted to electric power, what mass of Pu-238 would be required to power a 22 kW space probe for at least 150 y? [Use 238 for the atomic mass of Pu-238]
Jane, do you have an answer to this problem? I worked on this last evening but the answer I obtained did not seem reasonable to me so I didn't post it.
No. I worked out the problem and got around 45kg but Im not sure if its right.
To find the mass of Pu-238 required to power a space probe for 150 years, we need to calculate the total energy consumption of the probe and then convert it into the mass of Pu-238.
Step 1: Calculate the total energy consumption of the space probe.
We know the power (P) required to operate the space probe, which is 22 kW (or 22,000 Watts). We need to convert this power to energy by multiplying it by the time (t) it will be powered for, which is 150 years.
So, Total energy consumption (E) = Power (P) × Time (t)
E = P × t
E = 22,000 W × 150 years
Note: Since we are dealing with a long timescale, let's convert years to seconds. There are approximately 31,536,000 seconds in a year.
E = 22,000 W × 150 years × 31,536,000 seconds/year
Step 2: Calculate the number of alpha-decays.
We know the energy released by each decay (5.6 MeV) and its half-life (87.7 years). We can calculate the number of decays by dividing the total energy consumption by the energy released per decay.
Number of decays = Total energy consumption (E) / Energy released per decay
The energy released by each decay is given in MeV, so we need to convert it to Joules:
1 MeV = 1.6 × 10^-13 Joules
Energy released per decay = 5.6 MeV × 1.6 × 10^-13 Joules/MeV
Step 3: Convert the number of decays to mass of Pu-238.
The number of decays is directly proportional to the number of atoms of Pu-238, which is proportional to its mass.
Number of decays = Number of atoms of Pu-238 = Mass of Pu-238 (in grams) / Molar mass of Pu-238
The molar mass of Pu-238 is 238 grams/mole.
Step 4: Calculate the mass of Pu-238.
Rearranging the previous equation, we can solve for mass:
Mass of Pu-238 = Number of decays × Molar mass of Pu-238
Now, let's plug in the values and calculate the mass.
Mass of Pu-238 = (Number of decays × Molar mass of Pu-238)
= (Total energy consumption / Energy released per decay) × (Molar mass of Pu-238)
Note: We'll keep the molar mass of Pu-238 as 238 grams/mole.
Following these steps, we can find the mass of Pu-238 required to power the space probe for at least 150 years.