Two electron are moving towards each other with a velocity of #10^6 m/s# what will be the closest distance of approach between them?

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Answer 1 · 2018-03-20T07:00:07

#"2.53 Å"#

Total kinetic energy of electrons

#"K.E" = 2 × 1/2\ "mv"^2#

Potential energy of electrons

#"U" = ("ke"^2)/"r"#

When they approached closest distance (#"r"#) their total kinetic energy is converted into potential energy.

#"K.E = U"#

#2 × 1/2\ "mv"^2 = ("ke"^2)/"r"#

#color(blue)["r" = ("ke"^2)/("mv"^2)]#

#"r" = (9 × 10^9\ "Nm"^2//"C"^2 × (1.6 × 10^-19\ "C")^2)/(9.1 × 10^-31\ "kg" × (10^6\ "m/s")^2) = 2.53 × 10^-10\ "m" = "2.53 Å"#