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17-Phys-B1 Radiation Physics · December 2017

Question 5 of 7: Can Visible Light Photoeject an Electron from Sodium?

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. 98-Phys-B1 Radiation Physics, National Examination December 2017 — a three-hour open-book examination in which any non-communicating calculator is permitted (the candidate must record the calculator's make and model on the first sheet). The cover page states the exam has 7 questions worth a total of 74 points, of which only 60 points' worth need be answered for full marks; every question and sub-part is nonetheless answered in full below so the paper remains a complete study resource. The cover page also invites the candidate to submit a written statement of any assumptions made where a question is open to interpretation — this licence is used below in Question 1(a)–(b) (the historic DOE report's "roentgens per hour" reading is converted to absorbed dose using the standard air-kerma factor since no calibration medium is stated) and 1(e) (the Canadian nuclear-energy-worker annual effective-dose limit, 50 mSv/yr, is used to size the inspection-crew rotation since the source states no dose constraint of its own), and in Question 6(a) (counting-statistics uncertainty is taken as Poisson, $\sigma(C)=\sqrt{C}$, on the one-minute count reported in each row, since the source gives no separate counting-time datum). Question 6 also carries a genuine internal inconsistency between the table header's definition of $g(t)$ and the definition restated in part (c) — both readings and the resolution adopted are flagged where they occur.

Reference texts. K. S. Krane, Introductory Nuclear Physics (nuclear reaction kinematics, pair production, fission energetics); F. H. Attix, Introduction to Radiological Physics and Radiation Dosimetry (exposure–dose conversion, photon interactions, non-ionizing radiation); J. R. Cember and T. E. Johnson, Introduction to Health Physics, 5th ed. (radiation weighting factors, ALARA dose planning, decay-counting statistics); J. E. Turner, Atoms, Radiation, and Radiation Protection, 3rd ed. (neutron detectors, radioactive decay/in-growth kinetics, radiation protection principles).

Question 5: Can Visible Light Photoeject an Electron from Sodium? (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Work function of sodium $W=5.12$ eV; visible light spans approximately $\lambda=380$–700 nm (violet to red).

Find. Whether any visible-light photon carries enough energy to overcome $W$, supported by the photon energies at the two ends of the visible band and the threshold wavelength implied by $W$ itself.

Approach. Compute the photon energy $E=hc/\lambda$ at both ends of the visible spectrum and compare against $W$; equivalently, compute the threshold wavelength $\lambda_{\text{th}}=hc/W$ and check whether it falls inside the visible band.

  1. Photon energy at the high-energy (violet) end of the visible band. Using $hc=1240\ \text{eV}\cdot\text{nm}$ at $\lambda=380$ nm: $$E_{\text{violet}} = \frac{hc}{\lambda} = \frac{1240\ \text{eV}\cdot\text{nm}}{380\ \text{nm}}$$ $$\boxed{E_{\text{violet}} \approx 3.26\ \text{eV}}$$ which is well below $W=5.12$ eV.
  2. Threshold wavelength implied by the work function. $$\lambda_{\text{th}} = \frac{hc}{W} = \frac{1240\ \text{eV}\cdot\text{nm}}{5.12\ \text{eV}}$$ $$\boxed{\lambda_{\text{th}} \approx 242\ \text{nm}}$$ which lies deep in the ultraviolet, far shorter than even the shortest visible wavelength (380 nm).
  3. Conclusion. Since even the highest-energy visible photon (violet, 3.26 eV) falls well short of sodium's 5.12 eV work function, and the threshold wavelength (242 nm) lies entirely outside the visible band in the UV, no visible-light photon — regardless of the light's intensity — can eject an electron from a sodium atom. Only photons of wavelength shorter than about 242 nm (deep UV) can do so, in line with Einstein's photoelectric relation, where it is the photon energy (frequency), not the total light intensity, that determines whether emission occurs at all.
Question 5 — results
QuantityResult
$E$ at 380 nm (violet)≈ 3.26 eV
$E$ at 700 nm (red)≈ 1.77 eV
Threshold wavelength $\lambda_{\text{th}}$≈ 242 nm (deep UV)
Can visible light eject an electron?No – requires UV, not visible, light