The "radius of the hydrogen atom" is often taken to be on the order of about 10-10m. If a measurement is made to determine the location of the electron for hydrogen in its ground state, what is the probability of finding the electron within 10¬10m of the nucleus?
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- Alpha particles of mass m = 6.64 ✕ 10−27 kg and kinetic energy K = 905 keV are projected at a target nucleus. If the alpha particles have a de Broglie wavelength with the same value as the diameter of the target nucleus, determine the radius (in m) of the target nucleus.normalise the ground state of the quantum harmonic oscillator that you found in by calculating the value of c, for an alpha particle with a mass of 6.645 * 10 ^-27 kg and frequency of3.17 * 10^-8 hz u(x) = Ce ^-(mwx^2/2h)An electron is in the nth Bohr orbit of the hydrogen atom. (a) Show that the period of the electron is T = n3t0 and determine the numerical value of t0. (b) On average, an electron remains in the n = 2 orbit for approximately 10 ms before it jumps down to the n = 1 (ground-state) orbit. How many revolutions does the electron make in the excited state? (c) Define the period of one revolution as an electron year, analogous to an Earth year being the period of the Earth’s motion around the Sun. Explain whether we should think of the electron in the n = 2 orbit as “living for a long time.”
- A Hydrogen atom initially in its ground state i.e., n = 1 level, absorbs a photon and ends up in n = 4 level. (a) What must have been the frequency of the photon? Now the electron makes spontaneous emission and comes back to the ground state. (b) What are the possible frequencies of the photons emitted during this process?In Millikan's oil-drop experiment, one looks at a small oil drop held motionless between two plates. Take the voltage between the plates to be 2241 V and the plate separation to be 2 cm. The oil drop (of density 0.81 g/cm3) has a diameter of 4.0 ×10-6 m. Find the charge on the drop, in terms of electron units.The K series of the discrete x-ray spectrum of tungsten contains wavelengths of 0.018 5 nm, 0.020 9 nm, and 0.021 5 nm. The K-shell ionization energy is 69.5 keV. (a) Determine the ionization energies of the L, M, and N shells. L shell _keV M shell keV N shell _keV
- Suppose someone wanted to build a scale model of the atom with a nucleus 1.3 m in diameter.Randomized Variablesd = 1.3 m How far away would the nearest electron need to be in meters? Assume the orbital radius of an electron is 10-10 m, while the radius of the nucleus is 10-15 m.(a) A hydrogen atom has its electron in the n = 2 level. The radius of the electron's orbit in the Bohr model is 0.212 nm. Find the de Broglie wavelength of the electron under these circumstances. (b) What is the momentum, mv, of the electron in its orbit? kg-m/sSo Determine the distance between the electron and proton in an atom if the potential energy ?U of the electron is 15.4 eV (electronvolt, 1 eV =1.6×10−19=1.6×10−19 J). Give your answer in Angstrom (1 A = 10-10 m)
- If the radius of a calcium ion is 0.22 nm, how much energy does it take to singly ionize it? Give your answer in electron-volts (eV) with precision 0.1 eV. Give your answer to 2 significant digits.By using the principle of accuracy, he proved the impossibility of the electron being inside the nucleus, given that the radius of the nucleus is 1 x 10-14m.An electron was ejected from the surface of cesium metal with a speed of 6.74*10^5 m/s.Given that the threshold energy for the removal of an electron from the cesium metal is 2.90*10^-19J. Calculate the incident wavelength in nanometers. For this problem, I believe we use the KE=E photon-Eo. However, I am having trouble getting from the formula to the desired answer of 400 nm.