Calculating energy/work of a quantum

[chef99]

Homework Statement

1- Calculate the energy, in joules, of a quantum of light with a wavelength of 590nm.
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2- Will this colour be able to produce photoelectrons from the surface of a metal with a work function of 3.0 eV? Explain your reasoning.

2. Homework Equations
E = hf

v = fλ

3. The Attempt at a Solution

v = fλ

f = v/λ

f = 3.0 x10⁸m/s / 5.9 x10^-7m

f = 5.08 x10¹⁴HzE = hf

E = (6.63 x10^-34J)(5.08 x10¹⁴Hz)

E = 3.37 x10^-19J

Joules to eVs:

3.37 x10^-19J / 3.0 x10⁸mThe quantum will produce 3.37 x10-19 J or 2.11 eV of energy.
2-

As this quantum of energy was determined to have an energy value of 2.11 eV, and the work function of the metal is 3.0eV, then no, this colour will not produce photoelectrons as the energy produced is below the threshold of the metal’s surface.

I am confident in my answers to part 1 but I'm not sure if I explained part 2 correctly or not. Any feedback would be great.

 

[kuruman]

Part 2 is adequately explained.

 

[chef99]

Part 2 is adequately explained.

Ok thank you