Calculate the wavelength of an electron (m = 9.11 x 10-28 g) moving at 3.66 x 100 m/s. a) 1.81 x 10-10 m b) 2.76 x 10-9 m c) 5.03 x 10-10 m d) 5.52 x 10-9 m e) 1.99 x 10-10 m

option e = 1.99 × 10⁻⁶ m

Explanation:

Given data:

Mass of electron = 9.11 × 10⁻²⁸ g   or 9.11 × 10⁻³¹ Kg

Velocity = 3.66 × 100 m/s

Wavelength = ?

Solution:

Formula:

λ  = h / m. v

λ  = wavelength

h = planck's constant

m = mass

v = velocity

Now we will put the values in equation

λ  = h / m. v

λ  =  6.63 × 10⁻³⁴ Kg. m²/s  / 3.66 × 100 m/s . 9.11 × 10⁻³¹ Kg

λ  =  6.63 × 10⁻³⁴ Kg. m²/s / 3334.26  × 10⁻³¹ Kg .m/s

λ  = 1.99 × 10⁻⁶ m

E) 1.99 x 10^-10 m

We are given;

The mass of an electron (m)as 9.11 x 10^-28 g

Speed of the electron (v) is 3.66 x 10^6 m/s.

We are required to find the wavelength of the electron.

This can be done using the  De Broglies wavelength Formula:

λ = h/mv; where λ is the electron wavelength, v is the speed of the electron, m is the mass of the electron and h is the plank's constant (6.626×10^-34)

Therefore;

Wavelength = (6.626×10^-34)÷(9.11 x 10^-28 g × 3.66 x 10^6 m/s)

                    = 1.987 ×10^-10 m

                    = 1.99 × 10^-10 m

Therefore, the wavelength of an electron is 1.99 × 10^-10 m