Final answer:
The longest wavelength of light that will emit electrons from a metal with a work function of 2.10 eV is 624 nm, which falls in the visible range, specifically in the red part of the spectrum.
Step-by-step explanation:
The longest wavelength of light that will emit electrons from a metal can be calculated using the equation:
λ = hc/E,
where λ is the wavelength, h is the Planck's constant (6.63 x 10⁻³⁴ J·s), c is the speed of light (3.00 x 10⁸ m/s), and E is the work function of the metal in Joules.
Converting the work function from electron volts (eV) to Joules:
E = 2.10 x 1.60 x 10⁻¹⁹ J = 3.36 x 10⁻¹⁹ J.
Plugging in the values to the equation:
λ = (6.63 x 10⁻³⁴ J·s) / (3.00 x 10⁸ m/s) / (3.36 x 10⁻¹⁹ J) = 6.24 x 10⁻⁷ m = 624 nm.
Therefore, the longest wavelength of light that will emit electrons from the metal with a work function of 2.10 eV is 624 nm. This wavelength is in the visible range, specifically in the red part of the spectrum.