# Question #88966

##### 2 Answers

#### Explanation:

The idea here is that your particle has an associated **de Broglie wavelength** that depends on its **momentum**,

- the
massof the particle- the
velocityof the particle

**SIDE NOTE** *The problem wants you to use speed instead of velocity, but keep in mind that velocity and speed are not the same thing*

More specifically, the momentum of the particle is given by the equation

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

Here

#m# is the mass of the particle#v# is its velocity

The de Broglie wavelength is given by the equation

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

Here

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

Now, the problem tells you that the aprticle is moving at

#c = 3.0 * 10^8"m s"^(-1)#

This means that the speed of the particle will be equal to

#v = 9.0/10 * c = 9.0/10 * 3.0 * 10^8"m s"^(-1)#

#v = 2.70 * 10^8"m s"^(-1)#

Use the de Broglie wavelength to calculate the *momentum* of the particle

#lamda = h/p implies p = h/(lamda)#

In order to be able to use the wavelength given to you, you must express Planck's constant using the fact that

#"1 J" = "1 kg m"^2 "s"^(-2)#

This means that you have

#h = 6.626 * 10^(-34) "kg m s"^color(red)(cancel(color(black)(-2))) * color(red)(cancel(color(black)("s")))#

#h = 6.626 * 10^(-34)"kg m"^2"s"^(-1)#

Now you're ready to plug in your value

#p = (6.626 * 10^(-34)"kg m"^color(red)(cancel(color(black)(2)))"s"^(-1))/(1.5 * 10^(-15)color(red)(cancel(color(black)("m")))) = 4.417 * 10^(-19)"kg m s"^(-1)#

Now rearrange the equation that describes the particle's momentum to solve for

#p = m * v implies m = p/v#

Plug in your values to find

#m = (4.417 * 10^(-19) "kg" color(red)(cancel(color(black)("m"))) color(red)(cancel(color(black)("s"^(-1)))))/(2.70 * 10^(8)color(red)(cancel(color(black)("m"))) color(red)(cancel(color(black)("s"^(-1))))) = color(darkgreen)(ul(color(black)(1.6 * 10^(-27)"kg")))#

The answer is rounded to two **sig figs**.

#### Explanation:

I suppose we could use:

where:

(If your going to use this formula, the units must be exact and if they are not you must convert them)

and for us,

The mass is of the particle is