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A level: Radioactivity Questions

Q19. A Radioisotope Thermonuclear Generator (RTG) is a device that uses some of the energy from radioactive decay to generate electricity.

The Mars rover Curiosity includes an RTG that contains plutonium-238.

The plutonium undergoes alpha decay and some of the energy is used to generate about 100 W of electrical power.

(a) Complete the equation for the alpha decay of plutonium-238.

the first mark is for the nucleon numbers correct

the second mark is for the correct proton number of the alpha particle

[2 marks]

(b) Only 6% of the energy from the decay is used to generate electricity.

Calculate the rate at which energy is transferred from the decay of plutonium-238 on Curiosity.

6% of power = 100W

100% of power = 100/0.06

rate at which energy is transferred from the decay = 1700 W

[1 mark]

(c) The RTG has a constant output voltage of 32 V.

Calculate the current when the output power is 100 W.

P = IV

100 = I x 32

I = 100/32

I = 3.1 A

[1 mark]

(d) Calculate the maximum number of components, each of resistance 45 Ω, that can be connected in parallel across the RTG before the maximum output power is reached.

For each parallel strand:

V = IR

I = V/R

I = 32/45 = 0.71 A

For total parallel circuit I = 3.1 A

Number of strands = 3.1/0.71 = 4.4

Therefore a maximum of 4 (must be rounded to a whole number)

components can be connected in parallel.

 

Alternative Method: use of the power formula

P = V2/R

P = 322/45

P = 23W

Number of components 100/23 = 4.3; therefore a maximum of 4 components can be used.

[2 marks]

(e) The alternative to using an RTG is to use a solar panel.

A typical solar panel installation on a house roof in the UK provides about 1000 kW h of electricity each year.

Calculate the average electrical power output of the installation.

1000 kWh = P x 365 x 24

P = 1000/(365 x 24)

P = 0.114 kW

P = 114 W

OR

energy = 1000 kW h

E =1000 x 1000 x 3600 = 3.6 x 109 J

Average power = 3.6 x 109/(365 x 24 x 3600) = 114 W

[2 marks]

(Total 8 marks)