Question 1.35 - Chemistry: Molecular Nature Of Matter And Change

Question

The speed of light in a vacuum is $\mathbf{2}\mathbf{.}\mathbf{998}\mathbf{\times }{\mathbf{10}}^{\mathbf{8}}\mathbf{m}\mathbf{/}\mathbf{s}$ . What is its speed in (a) km/h; (b) mi/min ?

Step-by-Step Solution

Answer

Answer

 

(a) The speed of light in a vacuum in the units of km/h is  $1.079\times {10}^9\mathrm{km}/\mathrm{h}$.

(b) The speed of light in a vacuum in the units of mi/min is $1.118\times {10}^7 \mathrm{mi}/\min$ .

Convert the speed of light from m/s to km/h

The unit conversion equation that shows the relation between kilometers and meters can be shown as follows:

1km = 10³m 

   $$\begin{gathered} \mathrm{The} \mathrm{conversion} \mathrm{factor} \mathrm{used} \mathrm{to} \mathrm{convert} \mathrm{meters} \mathrm{to} \mathrm{kilometers} \mathrm{is} \mathrm{as} \mathrm{follows}: \\ \frac{1\mathrm{km}}{{10}^3\mathrm{m}} \\ \mathrm{The} \mathrm{unit} \mathrm{conversion} \mathrm{equation} \mathrm{that} \mathrm{relates} \mathrm{between} \mathrm{seconds} \mathrm{and} \mathrm{minutes} \mathrm{is} \mathrm{given} \mathrm{below}: \\ 1\min = 60\mathrm{s} \\ \mathrm{The} \mathrm{time} \mathrm{ratio} \mathrm{for} \mathrm{converting} \mathrm{minutes} \mathrm{to} \mathrm{seconds} \mathrm{is} \mathrm{written} \mathrm{as} \mathrm{follows}: \\ \frac{60\mathrm{s}}{1\min } \\ \mathrm{The} \mathrm{unit} \mathrm{conversion} \mathrm{equation} \mathrm{that} \mathrm{describes} \mathrm{the} \mathrm{relationship} \mathrm{between} \mathrm{minutes} \mathrm{and} \mathrm{hours} \mathrm{is} \mathrm{given} \mathrm{below}: \\ 1\mathrm{h} = 60\min \\ \mathrm{The} \mathrm{unit} \mathrm{conversion} \mathrm{factor} \mathrm{for} \mathrm{converting} \mathrm{hours} \mathrm{to} \mathrm{minutes} \mathrm{is} \mathrm{written} \mathrm{as} \mathrm{follows}: \\ \frac{60\min }{1\mathrm{h}} \\ \mathrm{The} \mathrm{unit} \mathrm{analysis} \mathrm{setup} \mathrm{for} \mathrm{converting} \mathrm{from} \mathrm{m}/\mathrm{s} \mathrm{to} \mathrm{km}/\mathrm{h} \mathrm{can} \mathrm{be} \mathrm{written} \mathrm{as} \mathrm{follows}: \\ \frac{2.998\times {10}^{8}m}{1s} \times \frac{1km}{{10}^{3}m} \times \frac{60s}{1min} \times \frac{60min}{1h} = 1.079\times {10}^9 km/h \\ \mathrm{Hence}, \mathrm{the} \mathrm{speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{a} \mathrm{vacuum} \mathrm{is} 1.079\times {10}^9 \mathrm{km}/\mathrm{h} \end{gathered}$$ 

Convert the speed of light from m/s to mi/min .

 

The equation for the relationship between miles and meters is shown below:

1mi = 1609m

 $$\begin{gathered} \mathrm{The} \mathrm{conversion} \mathrm{ratio} \mathrm{for} \mathrm{converting} \mathrm{from} \mathrm{meters} \mathrm{to} \mathrm{miles} \mathrm{is}, \\ \frac{1\mathrm{mi}}{1609\mathrm{m}} \\ \mathrm{By} \mathrm{using} \mathrm{the} \mathrm{necessary} \mathrm{conversion} \mathrm{factors}, \mathrm{the} \mathrm{unit} \mathrm{analysis} \mathrm{setup} \mathrm{is}, \\ \frac{2.988\times {10}^{8}m}{1s}\times \frac{1mi}{1609m}\times \frac{60s}{1min} = 1.118\times {10}^7 mi/min \\ \mathrm{Therefore}, \mathrm{the} \mathrm{speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{a} \mathrm{vacuum} \mathrm{in} \mathrm{the} \mathrm{units} \mathrm{of} \mathrm{mi}/\min \mathrm{is} 1.118\times {10}^7 \mathrm{mi}/\min . \end{gathered}$$