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
Truong-Son N.
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...

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