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 × 10² s⁻¹
c 1.9 × 10⁶ s⁻¹
d 5.6 × 10¹⁴ s⁻¹

Explanation:

Step1: Recall the formula

The relationship between the speed of light ($c$), wavelength ($\lambda$), and frequency ($
u$) is $c = \lambda
u$. The speed of light $c = 3\times10^{8}\,m/s$.

Step2: Solve for frequency

Rearrange the formula 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:

$$ u=\frac{3\times 10^{8}}{5.4\times 10^{-7}}=\frac{3}{5.4}\times10^{8 + 7}\approx0.556\times10^{15}=5.56\times 10^{14}\,s^{-1}$$

Answer:

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