1. Surface plasmon heating of gold nanoparticles. (a) Au nanoparticles of diameter 7 nm absorb at their surface plasmon resonance of 520 nm. Calculate the energy of a photon of 520 nm light in Joules. (b) The heat capacity of gold is C = 0.129 J/(g·K). The change in energy associated with heating gold is ?U = mC?T, where m is the mass. Calculate ?U in Joules for a 20°C increase in the temperature of a single, 7 nm-diameter Au nanoparticle. (The density of Au is 19.30 g/cm³. Note that you calculated the mass of this nanoparticle on Problem 1(a) of the previous homework.) (c) If all of the absorbed light is converted to heat, how many photons are needed to increase the temperature by 20°C for hyperthermia cancer treatment? (In practice, more photons are needed than calculated here, because heat is also transferred from the nanoparticles to the surrounding medium.)
Added by Thomas R.
Close
Step 1
626 x 10^-34 J s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of the light. Plugging in the values, we get: E = (6.626 x 10^-34 J s)(3.00 x 10^8 m/s)/(520 x 10^-9 m) E = 3.82 x 10^-19 J So the energy of a photon of 520 nm light is 3.82 x Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 98 other Physics 103 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
1.1 Show that in an atom, the photons in a 1240 nm infrared beam possesses energies of 1.00 eV. (5) 1.2 Determine the energy of a photon of blue light of wavelength 450 nm. (6) 2.1 Determine the wavelength of photon emitted when an electron moves from n = 2 orbit to n = 1 orbit in a gold atom. If Z is the atomic number, and for gold Z = 79. Also, by how much energy will the bombarding electrons excite the gold atom to radiate this emission line? (7) 2.2 Determine the energy and frequency of the radiation emitted when an electron falls from n = 4 to n = 2 in a hydrogen atom. [Take m = 9.1×10⁻³¹kg, εₐ = 8.85×10⁻¹²C²./Nm] (6) 3.1 The uncertainty in the velocity V of a moving electron of mass 10⁻⁴⁰ kg is 2 x10⁶m/s. Calculate the uncertainty of the simultaneous measurement of its position X. [Take 6. 63 x10⁻³⁴] (6)
Bhushan K.
This problem is about how strongly matter is coupled to radiation, the subject with which quantum mechanics began. For a simple model, consider a solid iron sphere $2.00 \mathrm{~cm}$ in radius. Assume its temperature is always uniform throughout its volume. (a) Find the mass of the sphere. (b) Assume the sphere is at $20.0^{\circ} \mathrm{C}$ and has emissivity 0.860 . Find the power with which it radiates electromagnetic waves. (c) If it were alone in the Universe, at what rate would the sphere's temperature be changing? (d) Assume Wien's law describes the sphere. Find the wavelength $\lambda_{\max }$ of electromagnetic radiation it emits most strongly. Although it emits a spectrum of waves having all different wavelengths, assume its power output is carried by photons of wavelength $\lambda_{\max }$ Find (c) the energy of one photon and (f) the number of photons it emits each second.
Adi S.
Review. This problem is about how strongly matter is coupled to radiation, the subject with which quantum mechanics began. For a simple model, consider a solid iron sphere $2.00 \mathrm{cm}$ in radius. Assume its temperature is always uniform throughout its volume. (a) Find the mass of the sphere. (b) Assume the sphere is at $20.0^{\circ} \mathrm{C}$ and has emissivity $0.860 .$ Find the power with which it radiates electromagnetic waves. (c) If it were alone in the Universe, at what rate would the sphere's temperature be changing? (d) Assume Wien's law describes the sphere. Find the wavelength $\lambda_{\max }$ of electromagnetic radiation it emits most strongly. Although it emits a spectrum of waves having all different wavelengths, assume its power output is carried by photons of wavelength $\lambda_{\max }$. Find (e) the energy of one photon and (f) the number of photons it emits each second.
Penny R.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD