The 23rd-century starship enterprise uses a substance called dilithium crystals as its fuel.
a) Assuming this material is the result of fusion, what is the product of the fusion of two 6-Li Nuclei?
b) How much energy is released per kilogram of dilithium formed? (Mass of one 6-Li atom is 6.015121 amu.)
for a) I initially thought it would be 6-Li-3 + 6-Li-3 -> 12-C-6, but it’s not true. Then I tried 6-Li-3 + 6-Li-3 -> 4He2+ 4-He-2 + 4-He-2 but that is also not true. I have no idea how to come up with the fusion product.. please help!
for part b, the question wants the answer in J/kg. This, to me, does not make sense because J is already Kg*m^2*s^-2. It is like having two kg units and they cancel each other.
Anyhow, I wrote two lithium atomic mass equals to 3 helium atomic mass: (6.015121*2) = 3(4.002603) + mass defect.
then I convert the unit of mass defect from amu to kg by multiplying (1.66054*10^-27) and then I multiply again with (3.0*10^8)^2. (e=mc^2 formula.)
Could you please tell me what I did wrong? thank you in advance!
✅ Answers
Answerer 1
“for a) I initially thought it would be 6-Li-3 + 6-Li-3 -> 12-C-6, but it’s not true.”
Why not? Seems right to me.
“for part b, the question wants the answer in J/kg. This, to me, does not make sense because J is already Kg*m^2*s^-2.”
Yeah, the unit is equal to (m/s)^2 – that is, the same units as c^2. But this is a bit perverse. The unit is J/kg, as in how many joules do you get for every kilogram? No need to simplify this unit; it is what it is. Such a measure of specific energy is going to be useful for any kind of fuel, from coal to gasoline to battery power to antimatter.
Answerer 2
I don’t know about part b, but for part a, you can try 12-C-6 alone. (The question is only asking for reaction product, not the whole equation.)