Question

Calculate the velocity of an electron having a length of 3.55 × 10-11 m. [Mass of electrons = 9.1 × 10 -31 kg]​

Answer 1

Given:

Wavelength of Electron Wave = 3.55 × 10^(-11)m.

To find:

Velocity of electron.

Calculation:

As per De-Broglie Equation :

$\therefore \: \lambda = \dfrac{h}{mv}$

Putting available value in SI units ;

$= > \: 3.55 \times {10}^{ - 11} = \dfrac{6.62 \times {10}^{ - 34} }{9.1 \times {10}^{ - 31} \times v}$

$= > \: v= \dfrac{6.62 \times {10}^{ - 34} }{9.1 \times {10}^{ - 31} \times 3.55 \times {10}^{ - 11} }$

$= > \: v= \dfrac{6.62 \times {10}^{ 8} }{9.1 \times 3.55 }$

$= > \: v = 0.204 \times {10}^{8} \: m {s}^{ - 1}$

$= > \: v = 2.04 \times {10}^{7} \: m {s}^{ - 1}$

So, final answer is

$\boxed{ \sf{ \large{\: v = 2.04 \times {10}^{7} \: m {s}^{ - 1} }}}$

Answer 2

we have to calculate the velocity of an electron having a length of 3.55 × 10¯¹¹ m. where mass of electron, m = 9.1 × 10¯³¹ kg

To find : minimum seperation (length ) between two consecutive crests or toughs is known as wavelength. here given length is wavelength of wave motion of electron.

from De - Broglie's wavelength equation,

λ = h/mv

⇒v = h/mλ

where h is plank's constant i.e., h = 6.63 × 10¯³⁴ Js ,

mass of electron, m = 9.1 × 10¯³¹ kg

and wavelength, λ = 3.55 × 10¯¹¹ m

now, v = (6.63 × 10¯³⁴)/(3.55 × 10¯¹¹ × 9.1 × 10¯³¹)

= (6.63)/(3.55 × 9.1) × 10^8 m/s

= 0.2052 × 10^8 m/s

= 2.052 × 10^7 m/s

Therefore the velocity of electron is 2.052 × 10^7 m/s.