# Question #6ec4f

##### 1 Answer

#### 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))) -># thede Broglie wavelength

Here

Now, the **momentum** of the astronaut is directly proportional to its **velocity**, *speed*, and its **mass**,

#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**.