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

Answer:

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

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]:

$y^2=x^2+2x^2$

$y^2=3x^2$

$x=\sqrt{\frac{y^2}{3}}=0.2586 nm\approx 0.259 nm$

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