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]

Question

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]

Answer 1

To solve this problem, we need to calculate the total energy required to power the space probe for 150 years, and then determine how much mass of Pu-238 is needed.

First, let's find the energy required to power the space probe for 150 years. The power is given as 22 kW, and we can convert this to energy using the formula: Energy = power * time.

E = P * t

E = 22 kW * 150 years

Before we proceed further, let's convert 22 kW to the same energy unit as the decay energy of Pu-238 (MeV).

1 kW = 1000 J/s
1 J = 1 eV

So, 22 kW = 22,000 J/s = 22,000 eV/s. To convert eV to MeV, we divide by 10^6.

22,000 eV/s ÷ 10^6 = 0.022 MeV/s

Now, let's calculate the total energy required over 150 years:

E = 0.022 MeV/s * 365 days * 24 hours * 3600 seconds * 150 years

Make sure to convert all units to the same base units, so this equation will give us the total energy in MeV.

Now, let's calculate the mass of Pu-238 needed to produce this amount of energy.

We know that each alpha decay releases 5.6 MeV of energy, and we want to know how much Pu-238 is needed to produce a certain amount of energy. We can use the equation:

Energy released = mass of Pu-238 * energy released per decay

5.6 MeV = mass of Pu-238 * energy released per decay

Now, let's solve for the mass of Pu-238:

mass of Pu-238 = Energy required / energy released per decay

Plug in the calculated total energy required and the given energy released per decay:

mass of Pu-238 = (total energy required) / (5.6 MeV)

mass of Pu-238 = (calculated total energy required in MeV) / (5.6 MeV)

Finally, calculate the mass using the given atomic mass of Pu-238 (238 atomic mass units per mole):

mass of Pu-238 = (calculated total energy required in MeV) / (5.6 MeV) * (1 mole / 238 atomic mass units) * (238 atomic mass units / 6.022 * 10^23 atoms) * (1 atom / 1.66 * 10^-24 g)

Simplify the units and calculate the mass of Pu-238.