An electron is traveling at a speed of v o = 2 ∗ 10 7 cm/s. The speed is increased such that the increase in energy is △ E = 10 − 8 e V. Determine the increase in electron speed.

Question

An electron is traveling at a speed of       v    o    =  2  ∗      10    7   cm/s. The speed is increased such that the increase in energy is   △  E  =      10          −      8        e  V. Determine the increase in electron speed.

Bryson Carlson · Accepted Answer

Electron moving with a velocity   (      v    1    )  =  2  ×      10    7   cm/s or   2  ×      10    5   m/s  ∆  E  =      10          −      8        E  V    1  E  V  =  1.6  ×      10          −      19        J    ∆  E  =  1.6  ×      10          −      27        JChange in kinetic energy  =  1      /    2  m  (      v    2    2    −      v    1    2    )      v    2    =      v    1    +  ∆  v        v    2    2    =      v    1    2    +  (  ∆  v      )    2    +  2  ×  v  1  ×  ∆  v    ∆  v  &amp;lt;&amp;lt;      v    1          v    2    2    =      v    1    2    +  2  ×  ∆  v  ×      v    1  Substitute       v    2    2   in change in energy equation we get  ∆  E  =  m  ×      v    1    ×  ∆  vIncrease in speed   ∆  v  =  1.6  ×      10    −    27      /    (  9.11  ×      10          −      31        ×  2  ×      10    5    )  =  8.7815  ×      10          −      3        m      /    snew speed       v    2    =  200000.0088

An electron is traveling at a speed of v_o = 2 *10^7 cm/s. The speed is increased such that the increase in energy is triangle E = 10^-8 eV. Determine the increase in electron speed.

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