Question

The distance between the red and blue balls at the corners of this cube is0.448 nm :Calculate the distance between the red and green balls. Round your answer to significant digits, and be sure it has the correct unit symbol.

Answer 1

0.259 nm is the distance between the red and green balls.

Step-by-step explanation:

Let the distance between the red and green ball be = RG =x

Let distance between blue and red ball = RB =y = 0.448 nm

Let distance between blue and green ball = GB = z

In triangle RGB

`RB^2=RG^2+GB^2` ( Pythagoras theorem)

`y^2=x^2+z^2`..[1]

In triangle GOB

`GB^2=GO^2+OB^2` ( Pythagoras theorem)

GO = OB = sides of cube

`x^2+x^2=z^2`

`2x^2=z^2`..[2]

Using [2] in [1]:

`y^2=x^2+2x^2`

`y^2=3x^2`

`x=\sqrt{(y^2)/(3)}=0.2586 nm\approx 0.259 nm`

0.259 nm is the distance between the red and green balls.