Why do we say that ∆t= h/(2 ∆E) is a lower-bound estimate of the lifetime of an atomic state? Why isn’t that the exact or approximate value of the lifetime?
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Why do we say that ∆t= h/(2 ∆E) is a lower-bound estimate of the lifetime of an atomic state? Why isn’t that the exact or approximate value of the lifetime?
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- where ?∞ = 1.097 × 10^7 m−1is the Rydberg constant and ? is the atomic number (thenumber of protons found in the nucleus). Calculate the ground state energy of a triplyionised beryllium atom, Be3+ (a beryllium atom with three electrons removed).Calculate the binding energy E_n=1 in eV and the classical Bohr radius a_0 in Å for an electron in the K shell (n=1) in the centroid system of the following atoms and hydrogen-like ions:(a) hydrogen, deuterium, muonic hydrogen, myonium and positronium.(b) He+, C^(5)+, Mo^(41)+ and Pb^(81)+ Need solution ASAP!!! Thx in advance.The gravitational attraction between electron and proton in a hydrogen atom is weaker than the coulomb attraction by a factor of about 10-40. An alternative way of looking at this fact is to estimate the radius of the first Bohr orbit of a hydrogen atom if the electron and proton were bound by gravitational attraction. You will find the answer interesting.
- . Suppose a quanton's wavefunction at a given time is y(x) = A[1 + (x/a)2]-¹, where A is an unspecified constant and a = 4.0 nm. According to the table integrals dx √ [1 + (x/a)²]² = 1 + (x/a)²+2tan ¹ (2) If we were to perform an experiment to locate the quanton at this time, what would the probability of a result between x = 0 and x = 8.0 nm?The total probability of finding an electron in the hydrogen atom is related to the integral ∫ r2 e-2r/ao dr Where r is the distance of the electron from the nucleus and ao is the Bohr radius. Evaluate thisintegral.Please answer (i), (v), and (vi). Thank you! (i) Using Bohr model for atomic hydrogen, obtain energy levels for the 2s, 3s and 3p states in the actual number with the unit of [eV]. We consider a transition that electron in the 3p state emits a photon and make a transition to the 2s state. What is the frequency v of this photon ? (ii) Now we do not include electron spin angular momentum, and just estimate an effect of a magnetic field B on this transition (Normal Zeeman effect) with orbital angular momentum. How many lines of optical transition do we expect ? What is the interval of the frequency in the field B = 0.1 Tesla ? (iii) In this situation, we do not expect transition from 3s to 2s state if the electron is initially in the 3s state, Explain the reason. (iv) We now consider an effect of magnetic field B to a free electron spin (not in Hydrogen, but a free electron). The magnetic field of B = 1.0 Tesla will split the energy level into two (Zeeman) levels. Obtain the level…