Question

measured in meters, the wavelength of red light is about 8×10⁻⁷, and the wavelength of violet light is 4×10⁻⁷. the wavelength of red light is how many times longer than the wavelength of violet light? 8×10⁻⁷ m 4×10⁻⁷ m 2 times as long 4 times as long 10⁷ times as long 10² times as long

Explanation:

Step1: Set up the division

We need to find out how many times the wavelength of red - light is longer than that of violet - light. So we divide the wavelength of red light by the wavelength of violet light. The wavelength of red light is $8\times10^{-7}$ m and the wavelength of violet light is $4\times10^{-7}$ m. The division is $\frac{8\times10^{-7}}{4\times10^{-7}}$.

Step2: Use the quotient rule of exponents

According to the quotient rule $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$. Here $a = 8$, $b = 4$, $m=-7$ and $n = - 7$. So $\frac{8\times10^{-7}}{4\times10^{-7}}=\frac{8}{4}\times10^{-7-(-7)}$.

Step3: Simplify the fraction and the exponent

First, $\frac{8}{4}=2$. Second, $-7-(-7)=-7 + 7=0$. So $\frac{8}{4}\times10^{-7-(-7)}=2\times10^{0}$. Since any non - zero number to the power of 0 is 1 ($10^{0}=1$), the result is $2\times1 = 2$.

Answer:

A. 2 times as long