Question

The de broglie wavelength of an electron is 600 NM then what is the velocity of the electron

Answer 1

Explanation:

The de – Broglie wavelength of an electron is 600 nm. The velocity of the electron having the mass 9.1 X 10-31 Kg is. 0.0012 x 10+4 m/s.

Answer 2

Given: the wavelength of the electrons, λ = 600nm

To Find: the velocity of the electron, v.

Solution:

To calculate v, the formula used:

• λ = h / p
• λ = h / mv ( ∵ p = mv)

       here, λ is the de-Broglie wavelength

       h is the Planck's constant, h = 6.6 x 10⁻³⁴

       m is the mass of the electron i.e. m = 9.1 x 10⁻³¹ kg

       v is the velocity of the electron

Applying the above formula:

λ = h / mv

600 = 6.6 x 10⁻³⁴ / (9.1 x 10⁻³¹ x v)

First, convert 600nm into m:

1 nm = 10 ⁻⁹m

600 nm = 600 x  10 ⁻⁹

              = 6 x 10⁻⁷m

Putting the value in the formula for v:

6 x 10⁻⁷ = 6.6 x 10⁻³⁴ / (9.1 x 10⁻³¹ x v)

6 x 10⁻⁷ x 9.1 x 10⁻³¹ x v = 6.6 x 10⁻³⁴

54.6 x 10⁻³⁸ x v = 6.6 x 10⁻³⁴

v = 6.6 x 10⁻³⁴ / 54.6 x 10⁻³⁸

  = 0.12 x 10⁻³⁴  / 10⁻³⁸

  =  0.12 x 10⁻³⁴ x 10³⁸

  = 0.12 x 10⁴

v = 1.2 x 10⁵ m/s

Hence the velocity of electron is 1.2 x 10⁵ m/s.