Question

Question #6ec4f

Answer 1

`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.