Final answer:
The threshold frequency for sodium metal is calculated using the energy of the ejected electron and given photon frequency, where answer choice 'a' seems most likely correct, assuming this provided frequency is the threshold frequency for sodium.
Step-by-step explanation:
The threshold frequency for sodium can be found using the energy of the ejected electron and the formula E = hf - φ, where E is the kinetic energy of the ejected electron, h is Planck's constant, f is the frequency of the photon, and φ is the work function of the material (which is equivalent to the threshold energy). Since we're provided the kinetic energy (7.74 × 10⁻²⁰ J) and the frequency of the photon (6.66 × 10¹⁴ s⁻¹), we can rearrange the equation to solve for the work function φ. To check if the photoelectric effect will be observed with orange light, we need to know the frequency of the orange light and compare it to the threshold frequency. Generally, orange light has a frequency lower than the provided 6.66 × 10¹⁴ s⁻¹; thus, without its specific frequency, a concrete conclusion cannot be drawn. However, since the energy of the ejecting photon is specific, it is implied that this is indeed the threshold frequency, making answer choice 'a' the most likely correct answer.