Question

Electron have 1/10th velocity of light what is the wave length

Answer 1

Hey there !

Solution :

Speed of Light = 3 × 10⁸ m / s

Speed of electron = ( 1 / 10 ) × 3 × 10⁸ m / s

=> Speed of electron = 3 ×  10⁸ ×  10⁻¹

=> Speed of electron = 3 ×  10⁷ m / s

We know that,

Wavelength = Planck's Constant / Mass ×  Speed of Light

=> Planck's constant = 6.62 × 10⁻³⁴ m².kg / s

=> Mass of Electron = 9.1 × 10⁻³¹ kg

=> Wavelength = 6.62 × 10⁻³⁴ / 9.1 × 10⁻³¹ × 3 ×  10⁷

=> Wavelength = ( 6.62 / 9.1 × 3 ) × 10⁻³⁴ ⁺ ³¹ ⁻⁷

=> Wavelength = 0.2424 × 10⁻¹⁰ 

=> Wavelength = 2.42 × 10⁻⁹ m

10⁻⁹ m = 1 Nano meter

Hence Wavelength = 2.42 nm

Hope my answer helped :-)