• Question: How many atoms are there in a cheeseburger

    Asked by anon-267449 on 5 Nov 2020.
    • Photo: Zsolt Keszthelyi

      Zsolt Keszthelyi answered on 5 Nov 2020:

      It depends on whether it is double cheese and with or without mayonnaise.

      Let’s say this is a healthy cheeseburger with lettuce and tomato as well, weighing a total of about 250 grams.

      To simplify things, I will now assume that this leads to a quantity that I will call 10 moles.

      These 10 moles lead to 10 times the Avogadro number (6 x 10^23, a very large number, basically one million multiplied by one million, which is then multiplied by one million, and again multiplied by –almost- one million).

      The number of atoms depends on what molecules exactly there are, so it can vary a bit depending on the ingredients. For simplicity, let’s say that on average, the molecules in the cheeseburger have 4 atoms.

      Then we arrive with an estimate of 4 x 10 x 6 x 10^23 = 24 x 10^24. This is 24 followed by 24 zeros. A quite large number : )

    • Photo: Bradley Young

      Bradley Young answered on 5 Nov 2020:

      This is such a great question! It’s exactly the kind of thing that you would get asked in an interview for a place at university or for a job. In fact, in my oxford interview I was asked something very similar: “Can you estimate the number of nitrogen molecules in this room?”.

      Zsolt’s estimation method looks good to me but I think there is another method, let’s see if we get similar answers:

      Instead of using a weight-based approach, I’m going to use volume. If I estimate a cheeseburger as a cylinder and say it has a height of 6cm and a radius of 6cm then its volume is about 680cm^3 (6.8×10^-4 m3). An atom is roughly a sphere with a radius of 10^-10 metres so a volume of about 4×10^-30m3.

      So then if I do (6.8×10^-4)/(4×10^-30) I get roughly 10^26 atoms (100000000000000000000000000 atoms) which is a lot and pretty similar to Zsolt’s answer, which shows you there’s always more than one way to answer a question

    • Photo: Juan Pereiro Viterbo

      Juan Pereiro Viterbo answered on 5 Nov 2020:

      Well… as an average there are 125 atoms per cubic nanometer. The estimated volume of a cheeseburger is 236.59 cubic centimeters.There are 1000000000000000000000 (that is 10^21)cubic nanometers in a cubic centimeter. So approximate number of atoms in a cheeseburger are:
      29573750000000000000000000 atoms. I hope I have not make any mistake counting zeros… (that is supposed to be 2.9 10^25 atoms). That is, you have more atoms in a cheeseburgers than stars in the universe…

    • Photo: Daisy Shearer

      Daisy Shearer answered on 7 Nov 2020:

      This is an awesome question!

      So, if we say that an average cheeseburger weighs around 200g (I’m going for a single patty burger here!), we can use the handy mole calculation triangle that you might have seen in chemistry class: number of moles=mass/molar mass.

      Now that we’ve estimated the mass of the burger, we need the molar mass to find the number of moles. For simplicity’s sake, let’s say that most of the atoms in the burger are carbon because meat consists of mostly protein, which is made up of amino acids which are predominantly carbon atoms (with amine and carboxyl groups but we’ll ignore those for now as this is just an estimate).

      Carbon has a molar mass of 12g which we will use in our equation:

      number of moles = 200g/12gmol^-1 = 6.66666 mol.

      To find the number of atoms, we multiply the number of moles by Avogadro’s number: 6.6666mol x 6.022×10^23 = (roughly) 1×10^25 atoms.

      In full, that’s 10,000,000,000,000,000,000,000,000 atoms (that’s 10 septillion atoms)!

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