Question

The mass of an electron is 9.1X10(-31) Kg .If its K.E is 6 X 10(-30) J . Calculate its wavelength .​

Answer 1

Answer:

2.1×10^(11)m or 210 nanometers.

Explanation:

Mass of electron = 9.1 ×10^(-31) kg

Kinetic energy of electron = 6 ×10^(-30) J

》 K.E. = 1/2 mv^2

1/2 mv^2 = 6 ×10^(-30)

mv^2 = 6 ×2 ×10^(-30)

v^2 = 12 ×10^(-30)

v = _/12×10^(-30)

v = 3.464 × 10^(-15) m/s

》De broglie's matter wave hypothesis equation

wavelength = h/p or h/mv

here h is planck's constant which is 6.626 ×10^(-34)Js

and p is momentum of particle.

wavelength of given electron = h/mv

= 6.626 ×10^(-34) / 9.1×10^(-31)×3.464×10^(-15)

= 6.626 ×10^(-34+31+15) / 9.1×3.464

= 6.626 / 31.52 × 10^(12)

= 0.21 × 10^(12)

= 2.1 ×(11) m

= 210 nm.