Photoelectron, khối lượng rút gọn và kích thích nguyên tử
Đã giới thiệu| English | Ý nghĩa |
|---|---|
| reduced mass/rɪˈdjuːst mæs/ | khối lượng rút gọn |
| work function/wɜːk ˈfʌŋkʃn/ | công thoát |
| bremsstrahlung/ˈbremʃtrɑːlʊŋ/ | Continuous X-ray radiation from electrons slowing down in nuclear fields. |
Peaks at 4, 8 and 12 volts
- In a Franck–Hertz tube the current dips every 4 V. That is not three energy levels: electrons are losing the same 4 eV excitation once, twice, three times.
- GRE atomic physics tests the photoelectric effect, X-ray spectra, reduced mass 约化质量 and spin pairing.
Photoelectric effect
- $K_{\max} = h\nu - \phi$ above threshold $\nu_0 = \phi/h$, where $\phi$ is the work function 逸出功; stopping potential $eV_s = K_{\max}$, linear in $\nu$.
- Brighter light at fixed frequency gives more electrons (current), not faster ones.
$\nu = 8\times10^{14}$ Hz, $h = 4.136\times10^{-15}$ eV·s: $h\nu = 3.31$ eV. With $\phi = 2.0$ eV, $K_{\max} = 1.31$ eV and $V_s = 1.31$ V.
What does the change affect?
Separate maximum energy from photocurrent in the photoelectric effect.
4.0 eV photons on a surface with work function 2.3 eV. Stopping potential in V?
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
The maximum kinetic energy is $4.0 - 2.3 = 1.7$ eV, so a 1.7 V stopping potential halts the fastest electrons.
Threshold frequency for $\phi = 2.0$ eV, in units of $10^{14}$ Hz (two decimal places)?
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
$2.0 / 4.136\times10^{-15}$.
At a fixed frequency, doubling the light intensity doubles the number of photoelectrons but not their maximum kinetic energy.
Độ khó 1/5 · 100 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
True. More photons eject more electrons, but each photon has the same energy hf, so $K_{max} = hf - \phi$ is unchanged.
X-ray spectra
- Characteristic lines: an electron fills an inner-shell vacancy; sharp, set by the target element.
- Bremsstrahlung 轫致辐射: decelerating electrons give a continuum, ending at the tube energy $eV$. Both usually appear together.
Reduced mass
- Two-body atoms use $\mu = \dfrac{m_eM}{m_e + M}$; energies scale as $\mu Z^2$. Positronium: $\mu = m_e/2$, so its wavelengths are twice hydrogen's.
- Hund's rule: fill degenerate orbitals singly with parallel spins first. Carbon $2p^2$ and oxygen $2p^4$ both have $S = 1$.
Compared with hydrogen, positronium spectral wavelengths are
Độ khó 1/5 · 100 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
μ = mₑ/2 halves every energy.
Franck–Hertz
- Spacing $\Delta V$ means energy $e\Delta V$ lost per collision. Contact potentials shift the peaks, so use the spacing.
- 4 V spacing: 4 eV, and the excited atom emits at $1240/4 = 310$ nm.
Mercury Franck–Hertz dips are 4.9 V apart. Wavelength of the emitted photon in nm (nearest whole)?
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
A 4.9 eV photon has $\lambda = 1240/4.9 = 253$ nm (using $hc = 1240$ eV nm).
Recap
- $K_{\max} = h\nu - \phi$; intensity changes current only.
- Lines come from inner-shell transitions, the continuum from bremsstrahlung.
- Energies scale with $\mu$; Franck–Hertz spacing is one excitation energy.
- bremsstrahlung: Continuous X-ray radiation from electrons slowing down in nuclear fields.