numbat/examples/what_if_158.nbt

# Hot Banana
#
# I heard that bananas are radioactive. If they are radioactive, then
# they radiate energy. How many bananas would you need to power a house?
#
# https://what-if.xkcd.com/158/

# Bananas contain Potassium-40 with the following properties:

let halflife: Time = 1.25 billion years
let molar_mass: MolarMass = 40 g / mol

# 40-K has a natural occcurence of

let occurrence_40K = 0.0117%

# We can now compute the radioactivity of natural potassium

let decay_rate: Activity = ln(2) / halflife

let radioactivity: Activity / Mass =
    N_A × occurrence_40K × decay_rate / molar_mass -> Bq / g

print("Radioactivity of potassium: {radioactivity}")

# Next, we come to bananas

@aliases(bananas)
unit banana

# https://fdc.nal.usda.gov/fdc-app.html#/food-details/173944/nutrients

let potassium_per_banana = 451 mg / banana

let radioactivity_banana: Activity / Banana =
    potassium_per_banana × radioactivity -> Bq / banana

print("Radioactivity of a banana: {radioactivity_banana}")

# A single 40-K decay releases an energy of
# (https://commons.wikimedia.org/wiki/File:Potassium-40-decay-scheme.svg)

let energy_per_decay: Energy = 11 percent × 1.5 MeV + 89 percent × 1.3 MeV

# Finally: how many bananas do we need to power a single household?

let power_per_banana: Power / Banana =
    radioactivity_banana × energy_per_decay -> pW / banana

print("Power per banana: {power_per_banana}")

unit household

let power_consumption_household: Power / Household =
    3000 kWh per household per year

let bananas_per_household =
    power_consumption_household / power_per_banana -> bananas / household

print("Bananas per household: {bananas_per_household}")

# TODO: https://what-if.xkcd.com/158/ says this number should be around
# 300 quadrillion, but we only get 0.1 quadrillion. 300 quadrillion
# times "a couple of picowatt" would be an average power consumption of
# at least 300 kW / household, which seems … excessive.