Question

The mass of an electron is 9.1 x 10⁻³¹kg. If its K.E. is 3.0 × 10⁻²⁵J, calculate its wavelength.

Answer 1

Given, mass of electron = 9.1 × 10⁻³¹kg

K. E. = 3.0 × 10⁻²⁵J

\(\because\) K. E. = \(\frac{1}{2}\)mv²

v = \(\sqrt{\frac{2K.E}{m}}\) = \(\sqrt{\frac{2\times3.0\times10^{-25}kg\,m^2s^{-1}}{9.1\times10^{-31}\,kg}}\)

= 812 ms⁻¹

Now, apply de-Broglie equation,

Wavelength, \(\lambda\) = \(\frac{h}{mv}\)

= \(\frac{6.626\times10^{-34}Js}{9.1\times10^{-31}kg\times812\,ms^{-1}}\)

= 8967 × 10⁻¹⁰m

= 896.7 nm