Graphs

$E_{k_{max}}$ against $f$

Maximum kinetic energy against frequency

$E_{K_{max}}=hf-\Phi$

• Gradient: Planck Constant ($h$)
• $x$-intercept: Threshold frequency ($f_0$)
• $y$-intercept: $-(\text{Work Function})$ ($-\Phi$)

Graph of maximum kinetic energy of photoelectrons against frequency of EM radiation

$E_{k_{max}}$ against $\frac{1}{\lambda }$

Maximum kinetic energy against $\frac{1}{\text{Wavelength}}$

$E_{K_{max}}=hc\left(\frac{1}{\lambda }\right)-\Phi$

• Gradient: $\text{Planck constant}\times \text{speed of light}$ ($hc$)
• $x$-intercept: $\frac{1}{\text{Threshold wavelength}}$($\frac{1}{{\lambda }_0}$)
• $y$-intercept: $-(\text{Work Function})$ ($-\Phi$)

Graph of maximum kinetic energy of photoelectrons against inverse of wavelength of EM radiation

$E_{k_{max}}$ against $\lambda$

Maximum kinetic energy against wavelength

$E_{K_{max}}=\frac{hc}{\lambda }-\Phi$

• $x$-intercept: Threshold wavelength (${\lambda }_0$)
• Horizontal asymptote: $-(\text{Work Function})$ ($-\Phi$)

Graph of maximum kinetic energy of photoelectrons against wavelength of EM radiation

$V_s$ against $f$

Stopping potential against frequency

$V_s=\left(\frac{h}{e}\right)f-\frac{\Phi }{e}$

• Gradient: $\frac{\text{Planck Constant}}{\text{electronic charge}}$ ($\frac{h}{e}$)
• $x$-intercept: Threshold frequency ($f_0$)
• $y$-intercept: $-\left(\frac{\text{Work Function}}{\text{electronic charge}}\right)$ ($-\frac{\Phi }{e}$)

Graph of stopping potential against frequency

Derivation

$V_s=\frac{E_{k_{max}}}{e}$ $V_s=\frac{hf-\Phi }{e}$ $V_s=\left(\frac{h}{e}\right)f-\frac{\Phi }{e}$

$\lambda$ against $p$

de Broglie wavelength against momentum

$\lambda =\frac{h}{p}$

• Relationship: Inverse relationship (hyperbolic curve)
• Asymptotes: Both axes ($\lambda =0$ and $p=0$) act as asymptotes

Graph of de Broglie wavelength against momentum

$p$ against $\frac{1}{\lambda }$

Momentum against inverse de Broglie wavelength

$p=h\left(\frac{1}{\lambda }\right)$

• Gradient: Planck Constant ($h$)
• Intercept: Passes through the origin ($(0,0)$)

Graph of momentum against inverse de Broglie wavelength