Science homework Im not sure how to answer this 3 part question

Question

(2.5 points) 1. (a) When a metal was exposed to light at a frequency of 5.74 x 1015 s-1, electrons were emitted with a kinetic energy of 6.97 x 10-19 J. Determine the work function, in kJ/mol.

(1.5 points) 1. (b) What is the maximum wavelength of light that would cause the emission of a photoelectron? Express your answer in nanometres (nm).

(2.5 points) 1. (c) When an electron drops from the n = 11 to the n = 1 level in a B4+ cation, a photon of energy is emitted. Does this photon have sufficient energy to cause the ejection of an electron from the above metal (that is, the metal in part (a) and (b))? Support your answer with calculations and a one sentence explanation. Hint: You may use Z instead of Zeff in your calculation.

Answer 1

There's a lot here so I'm going to answer the first part, and maybe someone else will chime in for the 2nd half. If not, perhaps you can re-submit the 2nd part as a separate question and if I have time and see it, I'll answer it at a later time. Sorry, but don't have the time right now, but wanted to at least give you the first part.

KE = hν − ϕ

KE = 6.97x10^-19 J

h = Planks constant = 6.626x10^-34 Js

ν = frequency = 5.74x10¹⁵ s

Φ = work function

Solving for Φ

Φ = 3.11×10^-18J / electron

3.11x10^-18 J/electron x 6.023x10²³ electrons/mol x 1kJ/1000 J = 1872 kJ/mol

maximum wavelength:

E = hc/λ

3.11x10^-18 J = (6.626x10^-34 Js) (3x108 m/s) / λ

λ = 6.40x10^-8 m = 64.0 nm

(c) ∆E = RZ²(1/n_f² - 1/n_i²)

∆E = change in energy

R = 2.179x10^-18 J

Z = atomic number of B = 5

nf = final energy level = 1

ni - initial energy level = 11

∆E = 2.179x10^-18 J ( 5)² (1/11²- 1/1²)

∆E = 5.45x10^-17 J (0.00826 - 1) = 5.45x10-17 J (-0.992)

∆E = -5.41x10^-17 J

This energy is greater than the energy above (3.11x10^-18 J) and so should be sufficient to eject an electron from the metal in parts (a) and (b).

I strongly suggest that you check and double check my math as I've been known to make careless mistakes.