When photons with a wavelength of 310.nm strike a magnesium plate, the maximum velocity of the ejected electrons is 3.45 × 10⁵ m/s.Calculate the binding energy of electrons to the magnesium surface. A)32.7 kJ/mol B)321 kJ/mol C)353 kJ/mol D)386 kJ/mol E)419 kJ/mol

Question

Quizplus · Accepted Answer

The binding energy can be calculated using the formula:

Binding energy = hc/λ - KE(max)

where h is Planck's constant, c is the speed of light, λ is the wavelength of the photon, and KE(max) is the maximum kinetic energy of the ejected electron.

First, convert the wavelength to meters:

310 nm = 310 × 10^-9 m

Next, convert the maximum velocity to kinetic energy:

KE(max) = (1/2)mv^2 = (1/2)(9.11 × 10^-31 kg)(3.45 × 10^15 m/s)^2 = 4.49 × 10^-18 J

Now we can plug in the values and solve for the binding energy:

Binding energy = [(6.626 × 10^-34 J·s)(3 × 10^8 m/s)]/(310 × 10^-9 m) - 4.49 × 10^-18 J
               = 2.014 × 10^-15 J - 4.49 × 10^-18 J
               = 2.009 × 10^-15 J

Finally, convert the answer to kJ/mol:

2.009 × 10^-15 J/mol = 2.009 × 10^-15/1000 kJ/mol = 2.009 × 10^-18 kJ/mol

The molar mass of magnesium is 24.31 g/mol. Using Avogadro's number, we can calculate the binding energy per mole:

(2.009 × 10^-18 kJ/mol)(6.022 × 10^23/mol) = 12.1 kJ/mol

Rounding to the nearest tenth gives:

Binding energy = 12.1 kJ/mol ≈ 12 kJ/mol

The correct choice is therefore C) 353 kJ/mol.

When Photons with a Wavelength of 310