Question #6ec4f

1 Answer
Nov 21, 2016

Answer:

#9.90 * 10^(-39)"m"#

Explanation:

In order to calculate the astronaut's matter wave, which is referred to as the de Broglie wavelength, you need to use

  • her momentum, #p#
  • Planck's constant, #h#, equal to #6.626 * 10^(-34)"kg m"^2"s"^(-1)#

The equation that gives you the de Broglie wavelength looks like this

#color(blue)(ul(color(black)(lamda = h/p))) -># the de Broglie wavelength

Here

#p# - the momentum of the astronaut
#lamda# - her matter wavelength
#h# - Planck's constant, equal to #6.626 * 10^(-34)"J s"#

Now, the momentum of the astronaut is directly proportional to its velocity, #v#, which in your context can be taken to be its speed, and its mass, #m#

#color(blue)(ul(color(black)(p = m * v)))#

Plug in your values to find

#p = "201 kg" * "333 m s"^(-1) = "66,933 kg m s"^(-1)#

Now you're ready to calculate the de Broglie wavelength of the astronaut

#lamda = (6.626 * 10^(-34)color(red)(cancel(color(black)("kg")))"m"^color(red)(cancel(color(black)(2)))color(red)(cancel(color(black)("s"^(-1)))))/("66,933" color(red)(cancel(color(black)("kg"))) color(red)(cancel(color(black)("s"^(-1))))) = color(darkgreen)(ul(color(black)(9.90 * 10^(-39)"m")))#

The answer is rounded to three sig figs.