Question

If an electron is accelerated from rest through a potential difference of 9.9 kV, what is its resulting speed? (e = 1.60 × 10-19 C, k = 1/4πε0 = 8.99 × 109 N · m2/C2, m el = 9.11 x 10-31 kg) If an electron is accelerated from rest through a potential difference of 9.9 kV, what is its resulting speed? ( = 1.60 × 10-19 C, = 1/4π = 8.99 × 109 N · m2/C2, el = 9.11 x 10-31 kg) 4.9 × 107 m/s 3.9 × 107 m/s 2.9 × 107 m/s 5.9 × 107 m/s

Answer 1

Answer:

So speed of electron will be $5.89\times 10^{-7}m/sec$

Explanation:

We have given potential difference V = 9.9 KV

Charge on electron $e=1.6\times 10^{-19}$

So energy of electron $E=eV=1.6\times 10^{-19}\times 9.9\times 10^3=15.84\times 10^{-16}J$

This energy of electron will be equal to kinetic energy of electron

So $\frac{1}{2}mv^2=15.84\times 10^{-16}J$

$\frac{1}{2}\times 9.11\times 10^{-31}v^2=15.84\times 10^{-16}$

$v=5.89\times 10^{-7}m/sec$

So speed of electron will be $5.89\times 10^{-7}m/sec$

Answer 2

The energy of accelerated electron from rest is equal to the kinetic energy of electron. The resulting speed of the accelerated electron is $5.89\times10^{-7} \rm m/s$.

What is energy of a electron?

The energy of a electron is the product of potential difference and the charge of the electron. It can be given as,

$E=eV$

Here. $V$ is the potential difference.

Given information-

The value of potential difference is 9.9 kV.

It is known that the charge on one electron is $1.6\times10^{-19}$.

The energy of the electron is the product of potential difference and the charge of the electron.

Thus the energy of the electron is,

$E=9.9\times10^{3}\times1.6\times10^{-19}\\E=15.84\times10^{-16} \rm J$

The energy of the electron is $15.84\times10^{-16}$ joules.

The kinetic energy of electron is half of the product of mass and the square of its speed.

As the mass of the electron is $9.11\times10^{-31}$ kg. Thus the energy of electron is,

$E=\dfrac{1}{2}mv^2\\15.84\times10^{-16}=\dfrac{1}{2}\times9.11\times10^{-31}v^2\\v=5.89\times10^{-7} \rm m/s$

Hence the resulting speed of the accelerated electron is $5.89\times10^{-7} \rm m/s$.

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