Question

An electron is accelerated by a potential difference of 12000v.Its inital velocity is 10^-7 m/s.The final velocity of the electron will be

Answer 1

hence, final velocity of electron will be 6.4257 × 10^7 m/s

An electron is accelerated by a potential difference of 12,000 volts.

so, workdone by electric field on electron , W = eV [ here e is charge on electron ]

= 1.6 × 10^-19 C × 12000

= 19.2 × 10^-16 J

from conservation of work- energy theorem,

workdone = change in kinetic energy

⇒19.2 × 10^-16 = 1/2 × (9.1 × 10^-31) {v² - (10^-7)²}

⇒19.2 × 2 × 10^-16/(9.1 × 10^-31) = (v² - 10^-14)

⇒4.129 × 10^15 = v² - 10^-14

⇒4.129 × 10^15 + 10^-14 ≈ 4.129 × 10^15 = v² [ 10^-14 is comparably very small so it can be neglected ]

⇒v = √(41.29) × 10^7 m/s

⇒v = 6.4257 × 10^7 m/s

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Answer 2

$\huge\bold\purple{Answer:-}$

An electron is accelerated by a potential difference of 12,000 volts.

so, workdone by electric field on electron , W = eV [ here e is charge on electron ]

= 1.6 × 10^-19 C × 12000

= 19.2 × 10^-16 J

from conservation of work- energy theorem,

workdone = change in kinetic energy

⇒19.2 × 10^-16 = 1/2 × (9.1 × 10^-31) {v² - (10^-7)²}

⇒19.2 × 2 × 10^-16/(9.1 × 10^-31) = (v² - 10^-14)

⇒4.129 × 10^15 = v² - 10^-14

⇒4.129 × 10^15 + 10^-14 ≈ 4.129 × 10^15 = v² [ 10^-14 is comparably very small so it can be neglected ]

⇒v = √(41.29) × 10^7 m/s

⇒v = 6.4257 × 10^7 m/s