Homework1

# Homework1 - MSE 110 Problem Set 1 Problem 1 Photons emitted...

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MSE 110 Problem Set 1, Problem 1 Photons emitted by a red He-Ne laser have energy E=3.145×10 -19 Joules. What is the wavelength of these photons? (5 pts) [Answer in nm] Ans: λ ν c h h E = = where E=3.145×10 -19 J, c = 3 × 10 8 m /sec, and h = 6.626 × 10 -34 J·sec Therefore, nm m J m s J 632 10 632 10 145 . 3 sec 10 3 10 626 . 6 9 19 8 34 = × = × = λ Problem 2 A green laser pointer emits photons of energy E=2.35eV. What is the wavelength of these photons? (5 pts) [Answer in nm] Ans: An eV is the energy gained by an electron accelerated by a potential of 1 V. Therefore it is equal to the charge of the electron multiplied by 1 volt: E = 1 V×1.6·10 -19 C. Hence 1 eV=1.6·10 -19 Joules. The energy of a green photon in units of Joules is therefore: E = 2.35 × 1.6·10 -19 J = 3.76·10 -19 J And its wavelength is nm m J m s J 6 . 528 10 6 . 528 10 76 . 3 sec 10 3 10 626 . 6 9 19 8 34 = × = × = λ Problem 3 CO 2 lasers are very intense lasers used industrially to cut and weld metal parts. It is a dangerous laser because it emits a beam invisible to the human eye in the infrared region at a wavelength λ =10600 nm. What is the energy of these photons in eV. [Answer in eV] (5 pts) Ans: λ c h E = and 1eV=1.6·10 -19 J Therefore: eV eV J m m s J E 117 . 0 10 6 . 1 10 06 . 1 sec 10 3 10 626 . 6 19 5 8 34 = × × × = 1

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Problem 4 The work function of iron is Φ =4.31eV. Which of the following photons can extract an electron from an iron cathode and produce a current in a photoelectric experiment? (5pt) [Answer A, B, C, D] A- 256 nm B- 324 nm C- 954 nm D- 584 nm Ans: In order to extract an electron from an iron cathode a photon must have at least an energy E= Φ =4.31eV, hence the maximum photon wavelength to remove a electron from iron is: nm eV J eV m s J 288 10 6 . 1 31 . 4 sec 10 3 10 626 . 6 19 8 34 = × × × = λ Hence only photon A is energetic enough to extract an electron from iron.
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