Question

The wavelength of red light is 650 nanometers. how much bigger is the wavelength of a water wave that measures 2 meters?

Answer 1

Wavelength of red light = 650 nm

Here the unit is nanometer, nano means 10⁻⁹

And wavelength of water = 2m

1 nanometer = 10⁹ meter

So, 2 meter = 2 x 10⁹ nm and 650nm = 6.5 x 10⁻⁷ m

now you can see the difference how much wavelength of water is bigger than wavelength of red light.

if we find the difference between them

650 nm= .00000065 m

2m - .00000065m = 1.99999935

so, the water wave is ~1.99999935 meters larger than the red light wave

Answer 2

we know that

$1$ nanometer is equal to $10^{-9}$ meters

so

$650\ nm$------> convert to meters

by proportion

$\frac{1}{10^{-9}}\frac{nm}{m} = \frac{650}{x} \frac{nm}{m} \\ \\ x=650*10^{-9} \ nm\\ \\ x=6.5*10^{-7} \ m$

$Wave\ length\ of\ red\ light = 6.5*10^{-7}\ m$

$Wave\ length\ of\ a\ water = 2\ m$

To calculate how much bigger is the wavelength of a water

Divide $2\ m$ by $6.5*10^{-7}\ m$

so

$\frac{2}{6.5*10^{-7}} =3.08*10^{6}$

therefore

the answer is

$3.08*10^{6}\ times\ bigger$