Question

what is the speed of an electromagnetic wave with a frequency of 1.33 x 10^17 hz and a wavelength of 2.25 nm? * q (0.5 points)
3.00 x 10^8 m/s
2.99 x 10^17 m/s
5.91 x 10^25 m/s
1.69 x 10^-17 m/s
1.69 x 10^-26 m/s
5.91 x 10^16 m/s

Explanation:

Step1: Convert wavelength to SI unit

Convert 2.25 nm to meters. Since 1 nm = 10^{-9} m, then $\lambda=2.25\times10^{-9}$ m. The frequency $f = 1.33\times 10^{17}$ Hz.

Step2: Use wave - speed formula

The speed of a wave is given by the formula $v = f\lambda$. Substitute the values of $f$ and $\lambda$ into the formula: $v=(1.33\times 10^{17}\text{ Hz})\times(2.25\times 10^{-9}\text{ m})$.

Step3: Calculate the result

Using the rule of exponents $a^m\times a^n=a^{m + n}$, we have $v=(1.33\times2.25)\times10^{17+( - 9)}=2.9925\times 10^{8}\text{ m/s}\approx3.00\times 10^{8}\text{ m/s}$.

Answer:

$3.00\times 10^{8}\frac{m}{s}$