Answer:
B
Explanation:
We can use Planck's equation. Recall that:
[tex]\displaystyle E = h\nu[/tex]
Where h is Planck's constant and ν is the frequency.
We also have that:
[tex]\displaystyle \lambda \nu = c[/tex]
Where c is the speed of light and λ is the wavelength. Hence:
[tex]\displaystyle \nu = \frac{c}{\lambda}[/tex]
Therefore:
[tex]\displaystyle E= h\left(\frac{c}{\lambda}\right)[/tex]
Solving for λ yields:
[tex]\displaystyle \lambda = \frac{hc}{E}[/tex]
Hence substitute. Recall that h = 6.626 × 10⁻³⁴ Js and c = 2.998 × 10⁸ m/s:
[tex]\displaystyle \begin{aligned} \lambda & = \frac{(6.626\times 10^{-34}\text{ Js})(2.998\times 10^8\text{ m/s})}{4.56\times 10^{-19} \text{ J}} \left(\frac{1\times 10^9\text{ nm}}{1\text{ m}}\right) \\ \\ & = 436\text{ nm}\end{aligned}[/tex]
In conclusion, our answer is B.
