carbon-14 is produced in the atmosphere principally by

carbon-14 is principally formed by a nuclear fission reaction in the atmosphere,

 how?

 the process of the formation of the radiocarbon  carbon be summarized in three nuclear fission  process.

   High energy cosmic rays are constantly bombarding the earth atmosphere, what is meant by cosmic rays are light from heavenly bodies like stars, comets, galaxies etc.  this high energy rays  produces secondary particles when they hit the at atmosphere

 One of the secondary particles or rays  formed is energetic  neutron , this neutron undergo a nuclear reaction to produces the radio-carbon, which is carbon-14.

 The neutron can react with either nitrogen or oxygen  to produces the radio-carbon

 As shown in the equation below

¹ ₀n + ¹⁴ ₇N → ¹⁴ ₆C + ⁰ ₁p

  The above reactions shows that a high energy neutron bombarded  nitrogen-14 atom and  carbon-14 is formed.

Another similar reaction that can produce the radiocarbon is when the high energy neutron it’s a oxygen-16 , the equation below show the nuclear reaction.

¹ ₀n + ¹⁶ ₈0 → ¹⁴ ₆C + ¹ ₁p + ²₁d + energy

 Let us see if the equation is balanced, we have

1 + 16 = 17 mass number on the left hand side and 14 +2+1=17 , mass number balanced..

 Next is the atomic number

0+8 =8 on the left hand side and  6+1+1= 8 on the right hand side, atomic number balanced.

 Another possible reaction is

1 0n + 168O→ 32He + 14C	+   -14.6MeV	20+/

¹ ₀n + ¹⁶₈O →³ ₂He + ¹⁴₆C +  Energy

Is this equations balanced.

 On the left hand side  1+16 is 17 and 3+14 is 17 balanced

 And for the atomic numbers, 0+ 8 is 8 and 6 + is 8 balanced .