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- The root mean square speed of the hydrogen molecules at temperature t °C is given by 3x8.31 x (t+273) m 2 x 10-3 Calculate the de Broglie wavelength (in nanometers) of the hydrogen molecules at temperature 24 °C. The mass of the hydrogen molecule is 2 x 1.66 x 10-27 kg. Use two decimals in your answer.Calculate (a) the thermal wavelength, (b) the translational partition function of an Ar atom in a cubic box of side 1.00 cm at (i) 300 K and (ii) 3000 K.Q. 1. An X-ray beam of wavelength 0.71 A is diffracted by a cubic KCL crystal of density 1.99x10^3 Kgm-3. Calculate the interplanner spacing for (200) planes and glancing angle for the second order reflection from these planes. The molecular weight of KCL is 74.6 amu and the Avagadro’s numberis 6.023x10^26 Kg-1 mole-1.
- 2.1. Find the de Broglie wavelength of the following particles: (i) an electron in a semiconductor having average thermal velocity at T = 300 K and an effective mass of me = amo, where a is a constant, (ii) a helium atom having thermal energy at T = 300 K, (iii) an a-particle (He4 nucleus) of kinetic energy 10 MeV.Outline the steps leading to the formula for the number of photons with angular fre- quencies between w and w + dw in blackbody radiation at a temperature T: w? dw V n(w)dw = 2 x 272c3 ehw/kBT Show that n(w) has a peak at a frequency given by w = 1.59kgT/h. Show further that the spectral energy densities ux and uw peak at Amax = hc/(4.97KBT) and wmax = 2.82KBT/ħ, respectively.An infrared spectroscopy study of a diatomic molecule XY has given the following information: We = 2377.48 cm-'; weXe 96.22 cm-1; Be 1.9982 cm- and ae 0.0190 cm-1. (a) At what frequency (expressed in wavenumbers) would the highest energy line of the P-branch of the fundamental vibrational transition appear in the IR spectrum of the molecule? (a) At what frequency (expressed in wavenumbers) would the highest energy line of the P-branch of the first overtone vibrational transition appear in the IR spectrum of the molecule?
- At 293 K, the Bragg angle for X-ray peak (111) from a powdered gold metal specimen is 38.30o. If the same peak is detected at 493 K, calculate the angle. Assume gold metal has a coefficient of linear thermal expansion of 14.2 x10-6 K-1 and a length of 0.47 nm for its standard FCC unit cell.The emergence of line spectra from a gas when a current passes through it was an observed phenomenon waiting for an explanation in the early 20th century. The atomic line spectra coming from elements such as hydrogen had been analyzed since the late 19th century. By studying the wavelength of the emerging radiation of hydrogen, experimenters found (often by trial and error) that the wavelengths in those spectra were described by the formula 1 = R ( 1/2 - 1/2 ) where R is known as the Rydberg constant. It has a value of R=1.097 × 107 m-¹. The variables n₁ and no are integer numbers (n₁ = 1, 2, 3, 4, ...). As experiments continued, scientists began to see more and more characteristic lines emerging from the hydrogen spectrum. Each of them corresponded to a wavelength predicted by this formula with some integer values for m₁ and ₂. In 1913, Niels Bohr provided an explanation for the observations made in experiments by proposing that each electron in an atom had only certain allowable…The average speed of a hydrogen molecule at 20o C is 1930 m/s. What is the wavelength of the H2 molecule at this temperature?
- What is the surface temperature of Betelgeuse, a red giant star in the constellation of Orion, which radiates with a peak wavelength of about 970 nm? (b) Rigel, a bluish - white star in Orion, radiates with a peak wavelength of 145 nm. Find the temperature of Rigel’s surface.Recall from Section 14.3 that the average kinetic energy of an atom in a monatomic ideal gas is given by KE=(3/2)kT, where k = 1.38 x 10-23 J/K and T is the Kelvin temperature of the gas. Determine the de Broglie wavelength of a helium atom (mass = 6.65 x 10-27 kg) that has the average kinetic energy at room temperature (292 K). Number i 7.38E-11 Units mWhat is the d-spacing of an XRD of a BCC crystal corresponding to a peak at 50ᵒ when studied using 1.5406 Aᵒ wavelength X-ray?. If a = 14.5316 Aᵒ for the crystal, what are the Miller indices corresponding to this peak?