MCAT Chemical and Physical Foundations of Biological Systems Flashcards: 4e Photoelectric Effect Line Spectra

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This deck focuses on 4e Photoelectric Effect Line Spectra, giving you a quick way to review the definitions, rules, and examples that matter most for MCAT Chemical and Physical Foundations of Biological Systems.

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Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: State the formula for photon energy emitted or absorbed for a hydrogen transition $n_i\to n_f$.

Answer: $\Delta E=13.6\ \text{eV}\left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right)$. Energy difference between levels determines photon energy in transitions, positive for emission when $n_i>n_f$.

Flashcard 2: Which quantity must exceed the work function $\phi$ for photoemission to occur?

Answer: Photon energy $hf$ must be $\geq \phi$. Photoemission requires photon energy at least equal to work function to overcome electron binding energy.

Flashcard 3: Which hydrogen series corresponds to transitions ending at $n_f=1$?

Answer: Lyman series. Lyman series involves transitions to ground state, producing UV lines.

Flashcard 4: Which hydrogen series corresponds to transitions ending at $n_f=3$?

Answer: Paschen series. Paschen series involves transitions to n=3, producing infrared lines.

Flashcard 5: Which direction of transition produces emission: $n_i>n_f$ or $n_i<n_f$?

Answer: Emission occurs for $n_i>n_f$. Electron dropping to lower energy level releases photon energy equal to level difference.

Flashcard 6: What is the Bohr energy formula for hydrogen energy level $n$?

Answer: $E_n=-\frac{13.6\ \text{eV}}{n^2}$. Bohr model quantizes hydrogen electron energies, negative due to bound states relative to ionization.

Flashcard 7: What is the physical meaning of the stopping potential $V_s$ in a photoelectric experiment?

Answer: Retarding voltage that reduces photocurrent to zero. Stopping potential opposes kinetic energy of fastest photoelectrons, halting them at collector.

Flashcard 8: What is the physical meaning of the work function $\phi$ in the photoelectric effect?

Answer: Minimum energy required to eject an electron from a metal. Work function represents binding energy of least-bound electrons in metal surface.

Flashcard 9: What is the threshold frequency $f_0$ in terms of work function $\phi$?

Answer: $f_0=\frac{\phi}{h}$. Threshold frequency is work function divided by Planck's constant, where photon energy just equals $\phi$.

Flashcard 10: What is the photoelectric equation relating $K_{\max}$, $hf$, and work function $\phi$?

Answer: $K_{\max}=hf-\phi$. Maximum kinetic energy of photoelectrons equals photon energy minus work function, per Einstein's explanation.

Flashcard 11: What is the slope and $x$-intercept of a plot of stopping potential $V_s$ versus $f$?

Answer: Slope $\frac{h}{e}$; $x$-intercept $f_0=\frac{\phi}{h}$. From $V_s=\frac{h}{e}f - \frac{\phi}{e}$, slope is $h/e$ and x-intercept is threshold frequency.

Flashcard 12: Which direction of transition produces absorption: $n_i>n_f$ or $n_i<n_f$?

Answer: Absorption occurs for $n_i<n_f$. Electron jumping to higher energy level requires absorbing photon energy matching level difference.

Flashcard 13: What is the formula for photon energy in terms of frequency $f$?

Answer: $E=hf$. Photon energy equals Planck's constant times frequency, linking wave and particle properties of light.

Flashcard 14: What is the stopping potential relation between $K_{\max}$ and $V_s$ for an electron?

Answer: $K_{\max}=eV_s$. Maximum kinetic energy equals electron charge times stopping potential, converting KE to potential energy.

Flashcard 15: What is the threshold wavelength $\lambda_0$ in terms of work function $\phi$?

Answer: $\lambda_0=\frac{hc}{\phi}$. Threshold wavelength is Planck's constant times speed of light divided by work function, longest $\lambda$ for emission.

Flashcard 16: What is the formula for $V_s$ in terms of $hf$ and $\phi$?

Answer: $V_s=\frac{hf-\phi}{e}$. Stopping potential equals photon energy minus work function divided by electron charge, from $K_{\max}=eV_s$.

Flashcard 17: Identify the photon with higher energy: one with $\lambda=400\ \text{nm}$ or $\lambda=800\ \text{nm}$.

Answer: $\lambda=400\ \text{nm}$ photon has higher energy. Photon energy inversely proportional to wavelength, so shorter $\lambda$ has higher energy.

Flashcard 18: Identify what changes when light intensity increases at fixed $f>f_0$ in the photoelectric effect.

Answer: Photoelectron number (current) increases; $K_{\max}$ unchanged. Higher intensity provides more photons, ejecting more electrons and increasing current, but photon energy fixes $K_{\max}$.

Flashcard 19: Identify what changes when frequency $f$ increases at fixed intensity in the photoelectric effect.

Answer: $K_{\max}$ and $V_s$ increase; emission requires $f\geq f_0$. Higher frequency increases photon energy, raising $K_{\max}$ and $V_s$ if above threshold for emission.

Flashcard 20: Which graph is linear for photoelectric data: $K_{\max}$ vs $f$ or $K_{\max}$ vs intensity?

Answer: $K_{\max}$ vs $f$ is linear with slope $h$. $K_{\max}$ increases linearly with frequency per photoelectric equation, unlike independence from intensity.

Flashcard 21: What is the formula for the speed of light in terms of $\lambda$ and $f$?

Answer: $c=\lambda f$. Speed of light equals wavelength times frequency for electromagnetic waves in vacuum.

Flashcard 22: Which hydrogen series corresponds to transitions ending at $n_f=2$ (visible region)?

Answer: Balmer series. Balmer series involves transitions to n=2, yielding visible wavelengths.

Flashcard 23: What is the Rydberg formula for the wavelength of a hydrogen spectral line?

Answer: $\frac{1}{\lambda}=R\left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right)$. Rydberg formula derives from Bohr energy differences, with $R$ as constant for hydrogen spectral lines.

Flashcard 24: What is the slope and $y$-intercept of a plot of $K_{\max}$ versus $f$?

Answer: Slope $h$; intercept $-\phi$. From $K_{\max}=hf-\phi$, slope is Planck's constant and y-intercept is negative work function.

Flashcard 25: What is the formula for photon energy in terms of wavelength $\lambda$?

Answer: $E=\frac{hc}{\lambda}$. Photon energy is Planck's constant times speed of light divided by wavelength, derived from $E=hf$ and $c=\lambda f$.