what is the wavelength in meters for an x - ray with a frequency of 1.0×10^19 hz? give your answer in proper…

Explanation:

Step1: Recall the wave - speed formula

The wave - speed formula is $c = \lambda\nu$, where $c$ is the speed of light ($c = 3.0\times10^{8}\ m/s$), $\lambda$ is the wavelength, and $\nu$ is the frequency. We need to solve for $\lambda$.

Step2: Rearrange the formula for wavelength

Rearranging $c=\lambda\nu$ gives $\lambda=\frac{c}{\nu}$.

Step3: Substitute the given values

We know that $c = 3.0\times10^{8}\ m/s$ and $\nu=1.0\times 10^{19}\ Hz$. Substituting these values into the formula $\lambda=\frac{c}{\nu}$, we get $\lambda=\frac{3.0\times 10^{8}}{1.0\times 10^{19}}$.

Step4: Use the rule of exponents for division

When dividing numbers in scientific notation $a\times10^{m}$ by $b\times10^{n}$, we use the rule $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$. Here, $a = 3.0$, $b = 1.0$, $m = 8$, and $n = 19$. So $\lambda=\frac{3.0}{1.0}\times10^{8-19}=3.0\times10^{- 11}\ m$.

Answer:

Coefficient (green): $3.0$ Exponent (yellow): $-11$