Question

Violet light of wavelength 400 nm ejects electrons with a maximum kinetic energy of 0.860 eV from sodium metal. What is the binding energy of electrons to sodium metal?

a) 2.14 eV
b) 1.54 eV
c) 3.00 eV
d) 0.34 eV

Answer 1

The binding energy of electrons to sodium metal when violet light of wavelength 400 nm ejects electrons can be found using photoelectric effect principles. Upon calculation, the binding energy is approximately 2.24 eV, with the closest answer choice being 2.14 eV (a).

Step-by-step explanation:

To find the binding energy of electrons to sodium metal when violet light of wavelength 400 nm ejects electrons with a maximum kinetic energy of 0.860 eV, we can use the photoelectric effect equation: energy of the photon (E) = binding energy of electron (ϕ) + maximum kinetic energy of the electron (KE).

The energy of a photon can be calculated using the equation E = hc/λ, where h is Planck's constant (4.135667696 × 10-15 eV⋅s), c is the speed of light (approximately 3 × 108 m/s), and λ is the wavelength of the photon.

First, let's calculate the energy of the photon:

E = (4.135667696 × 10-15 eV⋅s) × (3 × 108 m/s) / (400 × 10-9 m)
= 3.10 eV

Now, apply the photoelectric effect equation:

3.10 eV = ϕ + 0.860 eV
ϕ = 3.10 eV - 0.860 eV
ϕ = 2.24 eV

The closest value to our calculated result is 2.14 eV, which makes choice (a) 2.14 eV the correct answer.