Question

a metal foil has a threshold frequency of 5.45 × 10¹⁴ hz. which of the colors of visible light have enough energy to eject electrons from this metal? green yellow blue orange violet red indigo

Explanation:

Step1: Recall the photoelectric effect principle

For electrons to be ejected from a metal, the frequency of the incident light must be greater than or equal to the threshold frequency of the metal. The threshold frequency of the metal is \(v_0 = 5.45\times10^{14}\text{ Hz}\).

Step2: List the frequencies of visible - light colors

The frequencies of visible - light colors (approximate values):

• Red: \(v_{red}\approx4.0 - 4.8\times 10^{14}\text{ Hz}\)
• Orange: \(v_{orange}\approx4.8 - 5.1\times 10^{14}\text{ Hz}\)
• Yellow: \(v_{yellow}\approx5.1 - 5.3\times 10^{14}\text{ Hz}\)
• Green: \(v_{green}\approx5.3 - 6.0\times 10^{14}\text{ Hz}\)
• Blue: \(v_{blue}\approx6.0 - 6.3\times 10^{14}\text{ Hz}\)
• Indigo: \(v_{indigo}\approx6.3 - 6.7\times 10^{14}\text{ Hz}\)
• Violet: \(v_{violet}\approx6.7 - 7.5\times 10^{14}\text{ Hz}\)

Step3: Compare frequencies

• For green: \(v_{green}\) (ranges from \(5.3\times 10^{14}\text{ Hz}\) to \(6.0\times 10^{14}\text{ Hz}\)). Some of the green light frequencies (\(v\geq5.45\times 10^{14}\text{ Hz}\)) can eject electrons.
• For yellow: \(v_{yellow}\leq5.3\times 10^{14}\text{ Hz}<5.45\times 10^{14}\text{ Hz}\), so yellow light cannot eject electrons.
• For blue: \(v_{blue}\geq6.0\times 10^{14}\text{ Hz}>5.45\times 10^{14}\text{ Hz}\), so blue light can eject electrons.
• For orange: \(v_{orange}\leq5.1\times 10^{14}\text{ Hz}<5.45\times 10^{14}\text{ Hz}\), so orange light cannot eject electrons.
• For violet: \(v_{violet}\geq6.7\times 10^{14}\text{ Hz}>5.45\times 10^{14}\text{ Hz}\), so violet light can eject electrons.
• For red: \(v_{red}\leq4.8\times 10^{14}\text{ Hz}<5.45\times 10^{14}\text{ Hz}\), so red light cannot eject electrons.
• For indigo: \(v_{indigo}\geq6.3\times 10^{14}\text{ Hz}>5.45\times 10^{14}\text{ Hz}\), so indigo light can eject electrons.

Answer:

green, blue, violet, indigo