Question

1. gamma rays: 2.5×10⁻¹² meters visible light: 5.0×10⁻⁷ meters how many times larger is the wavelength of visible light compared to gamma rays?

Explanation:

Step1: Set up the division

To find out how many times larger the wavelength of visible - light is compared to gamma rays, we divide the wavelength of visible light by the wavelength of gamma rays. So the expression is $\frac{5.0\times 10^{-7}}{2.5\times 10^{-12}}$.

Step2: Use the quotient - rule of exponents

The quotient - rule states that $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$. Here, $a = 5.0$, $b = 2.5$, $m=-7$ and $n = - 12$. First, calculate $\frac{a}{b}$: $\frac{5.0}{2.5}=2$. Then calculate $10^{m - n}=10^{-7-(-12)}=10^{-7 + 12}=10^{5}$.

Step3: Multiply the results

Multiply the results from the two previous steps: $2\times10^{5}$.

Answer:

$2\times10^{5}$