Question

An electron is projected with an initial speed  v_i = 2.90

Answer 1

intial potential energy = 0

intial kinetic energy = 0.5 * m_electron * ( 2.9 * 10^5)^2 = 4.205 * 10^10 * m_electron J

intial total energy = 4.205 * 10^10 * m_electron J

final kinetic energy = 0.5 * m_electron * (2* 2.9 * 10^5)^2 = 16.82 * 10^10 * m_electron J

final potential energy = k * q1 q2 / r = -9 * 10^9 * 1.6^2 * 10^-38 / r =   - 2.304 * 10^-28 / r J

so.. final total energy = 16.82 * 10^10 * m_electron     - 2.304 * 10^-28 / r

m_electron = 9.1 * 10^-31 kg

so.. now.. inital total eneryg = final

so.. 16.82 * 10^10 * m_electron     - 2.304 * 10^-28 / r   =   4.205 * 10^10 * m_electron

so..    2.304 * 10^-28 / r   = 12.615 * 10^10 * m_electron

so.. 2.304 * 10^-28 / r   = 12.615 * 10^10 * 9.1 * 10^-31 = 114.7965 * 10^-21

so.. distance r = 2.007029831 * 10^-9 m   = 2.007029831 nm