Question

what is the smallest frequency of light required to remove an electron from titanium metal by the photoelectric effect, if the binding energy of titanium is 3.14 × 10⁶ j/mol?
○ 7.87 × 10¹⁵ hz
○ 3.55 × 10¹⁵ hz
○ 1.33 × 10¹⁵ hz
○ 2.71 × 10¹⁵ hz

Explanation:

Step1: Calculate energy per atom

Use \(E=\frac{E_{mol}}{N_A}\), where \(E_{mol} = 3.14\times10^{6}\space J/mol\) and \(N_A=6.022\times 10^{23}\space mol^{-1}\)
\(E=\frac{3.14\times 10^{6}}{6.022\times 10^{23}}\space J\)
\(E = 5.214\times10^{-18}\space J\)

Step2: Use Planck's equation \(E = h

u\)
Rearrange for \(
u\), \(
u=\frac{E}{h}\), where \(h = 6.626\times10^{-34}\space J\cdot s\)
\(
u=\frac{5.214\times 10^{-18}}{6.626\times 10^{-34}}\space Hz\)
\(
u=7.87\times 10^{15}\space Hz\)

Answer:

\(7.87\times 10^{15}\space Hz\)