Use the de Broglie's Wave Equation to find the wavelength of an electron moving at 3 × 106 m/s. Please show your work. Note: h = Plank's constant (6.62607 x 10-34 J s) ?
1 Answer
Jun 15, 2018
As you know, the de Broglie wavelength for an object with mass is
#lambda = h/(mv)# ,where:
#h = 6.62607004 xx 10^(-34) "J"cdot"s"# is Planck's constant.
#m_e = 9.10938356 xx 10^(-31) "kg"# is the rest mass of an electron.#v# is the velocity it moves, in#"m/s"# .
Therefore:
#lambda = (6.62607004 xx 10^(-34) "J"cdot"s")/((9.10938356 xx 10^(-31) "kg") (3 xx 10^6 "m/s"))#
#= (6.62607004 xx 10^(-34) cancel"kg"cdot"m"^cancel(2)"/"cancel"s")/((9.10938356 xx 10^(-31) cancel"kg") (3 xx 10^6 cancel"m""/"cancel"s"))#
#= 2.42 xx 10^(-10) "m"#
or...
#2.42 xx 10^(-10) cancel"m" xx ("1 Å")/(10^(-10) cancel"m") = color(blue)"2.42 Å"# .
However, you only gave yourself one significant figure...