Question

electromagnetic radiation with a maximum wavelength of 540 nm(5.4×10^(-7) m) is needed for the study of the photoelectric effect in potassium atoms. what is the approximate frequency that corresponds to this wavelength?
a 1.8×10^(-15) s^(-1)
b 1.6×10^(2) s^(-1)
c 1.9×10^(6) s^(-1)
d 5.6×10^(14) s^(-1)

Explanation:

Step1: Recall the speed - wavelength - frequency formula

The speed of light $c$ is related to wavelength $\lambda$ and frequency $
u$ by the formula $c = \lambda
u$, where $c=3\times 10^{8}\ m/s$ and $\lambda = 5.4\times 10^{-7}\ m$.

Step2: Solve for frequency

We can re - arrange the formula $c = \lambda
u$ to get $
u=\frac{c}{\lambda}$. Substitute $c = 3\times 10^{8}\ m/s$ and $\lambda = 5.4\times 10^{-7}\ m$ into the formula: $
u=\frac{3\times 10^{8}}{5.4\times 10^{-7}}$.

Step3: Calculate the frequency

$
u=\frac{3\times 10^{8}}{5.4\times 10^{-7}}=\frac{3}{5.4}\times10^{8 + 7}\ s^{-1}\approx0.56\times 10^{15}\ s^{-1}=5.6\times 10^{14}\ s^{-1}$.

Answer:

D. $5.6\times 10^{14}\ s^{-1}$