Question

What is the wavelength of an electron moving with a speed of 5.97 x 106 m/s? An
electron has a mass of 9.11 x 10-31 kg.

Answer 1

Answer:

1) The first step in the solution is to calculate the kinetic energy of the electron:

KE = 1/2 mv^2

2) Next, we will use the de Broglie equation to calculate the wavelength:

λ = h / p

λ = h / √ 2mE

Explanation:

v = 5.97 × 106 m/s

m = 9.11 x 10^-31 kg.

h = 6.26 × 10 ^ -34 j. s

using this you can calculate your answer

Answer 2

Given: An electron has mass of $9.11 \times {10}^{ - 31}$ kg. It is moving with a speed of $5.97 \times {10}^{6}$ m/s.

To find: Wavelength of the electron

Explanation: Let mass of electron be denoted by m and its velocity be denoted by v.

m=$9.11 \times {10}^{ - 31}$ kg

v=$5.97 \times {10}^{6}$ m/s

The de-Broglie wavelength of an electron is given by the formula:

l = h/p where l is the wavelength, h is Planck's constant and p is the momentum of the electron.

Value of h= $6.6 \times {10}^{ - 34}$ J s

p is the momentum of the electron which is the product of the mass and its velocity.

p= Mass of electron * Velocity

=>$p = 9.11 \times {10}^{ - 31} \times 5.97 \times {10}^{6}$

=>$p = 54.39 \times {10}^{ - 25}$

Using formula given above:

=>$l = \frac{6.6 \times {10}^{ - 34} }{54.39 \times {10}^{ - 25} }$

=>$l = 0.12 \times {10}^{ - 34 + 25}$

=>$l = 0.12 \times {10}^{ - 9} m$

Therefore, the wavelength of the electron is $0.12 \times {10}^{ - 9} m.$