Electric breakdown (sparks) occur in air if the electric fieldreaches 3 × 10 6 N

Question

Electric breakdown (sparks) occur in air if the electric fieldreaches 3 × 106N/C. Atthis field strength, free electrons present in the atmosphere arequickly accelerated to such large speeds that upon impact withatoms they knock electrons off of the atom and thereby generate anavalanche of electrons. How far must a free electron move under theinfluence of the above electric field if it is to attain a kineticenergy of 3 × 10-19J(which issufficient to produce ionization)? Please help, I dont know how to start this! I will rate lifesaver! Thank you! Electric breakdown (sparks) occur in air if the electric fieldreaches 3 × 106N/C. Atthis field strength, free electrons present in the atmosphere arequickly accelerated to such large speeds that upon impact withatoms they knock electrons off of the atom and thereby generate anavalanche of electrons. How far must a free electron move under theinfluence of the above electric field if it is to attain a kineticenergy of 3 × 10-19J(which issufficient to produce ionization)? Please help, I dont know how to start this! I will rate lifesaver! Thank you!

Explanation / Answer

electric force F = qE, where q is the charge, and E is the electricfield. Also remember, the change in energy is equal to the work, which isF*distance = F*d = (qE)*d Thus, we want the kinetic energy, 3e-19 J, to equal qEd = (1.6e-19C)(3e6 N/C)(d) Thus, d = (3e-19 J)/[(1.6e-19 C)(3e6 N/C) = 6.25e-7 m, or 625nanometers.

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