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

E) 1.99 x 10^-10 m

Explanation:

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

option e = 1.99 * 10⁻⁶ m

Explanation:

Given dа ta:

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