# Question #ee4ab

##### 1 Answer

#### Answer:

#### Explanation:

This problem is more or less an exercise in algebraic manipulation because all you have to do here is to use the equation that describes the **de Broglie wavelength** of the particle

#color(blue)(ul(color(black)(lamda_ "matter" = h/(m * v)))) -># thede Broglie wavelength

Here

#lamda_ "matter"# is its de Broglie wavelength#h# isPlanck's constant, equal to#6.626 * 10^(-34)"J s"# #m# is the mass of the particle#v# is its velocity

In your case, you know that

#lamda_"matter" = 100 * v#

This implies that

#v = lamda_"matter"/100#

Plug this into the above equation to get

#lamda_"matter" = h/(m * lamda_"matter"/100)#

At this point, all you have to do is to isolate

#lamda_"matter" = 100 * h/(m * lamda_"matter"#

#lamda_"matter" * m * lamda_"matter" = 100 * h#

#lamda_"matter"^2 = (100 * h)/m#

Therefore, you can say that

#lamda_"matter" = sqrt((100 * h)/m)#

which is equivalent to

#color(darkgreen)(ul(color(black)(lamda_"matter" = 10 * sqrt(h/m))))#