# Question 0daec

Jan 21, 2016

$5 \times {10}^{14}$ wavelengths.

#### Explanation:

From the definition of velocity, $v = \frac{x}{t}$

$\therefore x = v t$

$= \left(3 \times {10}^{8} m / s\right) \left(1 s\right) = 3 \times {10}^{8} m$.

Thus by ratio and proportion, if one wavelength is 600nm, then $3 \times {10}^{8} m$ would represent $\frac{3 \times {10}^{8}}{600 \times {10}^{-} 9} = 5 \times {10}^{14}$ wavelengths.

Jan 21, 2016

$5 \cdot {10}^{14}$

#### Explanation:

The idea here is that you need to consider the speed of light constant and use its known value to calculate how many wavelengths would fit per meter of distance traveled.

As you know, the speed of light can be approximated to be equal to $3 \cdot {10}^{8} {\text{m s}}^{- 1}$. This means that every second light travels a distance of $3 \cdot {10}^{8}$ meters.

Now, a nanometer, or $\text{nm}$, is simply a very small subunit of a meter. More specifically, you need to have a total of ${10}^{9}$ nanometers in order to have $1$ meter.

The conversion factor between these two units will thus be

$\text{1 m" = 10^9"nm}$

At this point, a unit conversion will take you from meters to nanometers

3 * 10^8 color(red)(cancel(color(black)("m"))) * (10^9 "nm")/(1color(red)(cancel(color(black)("m")))) = 3 * 10^(17)"nm"

Since one wavelength covers $\text{600 nm}$, or $6 \cdot {10}^{2} \text{nm}$, it follows that light emitted by the laser will cover

3 * 10^(17) color(red)(cancel(color(black)("nm"))) * "1 wavelength"/(6 * 10^2color(red)(cancel(color(black)("nm")))) = color(green)(5 * 10^(14)"wavelengths")#

The answer is rounded to one sig fig, the number of sig figs you have for the wavelength of the emitted light.