We have discovered that an electron’s orbit must contain an integer number of de Broglie wavelengths. Explain why, under ordinary conditions, this makes it impossible for electrons to spiral in to merge with the positively charged nucleus.

Q: Given the value of Rydberg constant is 107m−1, the waves number of the lest line of the Balmer…

A: We know that: λ1= R(1/n12−1/n22)

Q: (a) Using the Bohr model, calculate the speed of the electron in a hydrogen atom in the n = 1, 2,…

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Q: What is the velocity of an electron with a deBroglie wavelength of 2.74 um ? Give your answer in m/s…

A: Approach to solving the question:Please see attached photos for detailed solutions. Thank you.…

Q: Q.2: Calculate the shortest wavelength for electron revolving in the fourth excited germanium atom,…

A: Given that:Q=4.8×10-19 CTranstition, n1=5→n2=3→n3=2

Q: (a) Using Bohr’s second postulate of quantization of orbital angular momentum show that the…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: The wave function for the 1 s state of an electron in the hydrogen atom is

A: Given ψ1s ρ = 1πa03 e-ρa0 Bohr radius = a0

Q: The time-independent w (r) = √ 1 P = wavefunction y of the ground state of the hydrogen electron is…

A:

Q: While studying the particle in a box in this chapter, you come up with what you think is a brilliant…

A: The energy of a particle is

Q: Singly ionized helium has a single orbiting electron, so the mathematicsof the Bohr hydrogen atom…

A: Given, Energy level for ionized helium, En=-54.4n2 ev

Q: What is the wavelength of the hydrogen Balmer Series photon for m=4 and n=2 using the Rydberg…

A:

Q: Using knowledge of electron structure and spacing of energy levels, explain why the energy of…

A: Solution: For hydrogen atoms, energy levels are given by,  En=-13.6 eV n2 here,  n is some integer…

Q: Compute the intrinsic line-width (Δλ) of the Lyman α line (corresponding to the n=2 to n=1)…

A: Let us first compute the uncertainty in the energy i.e. ΔE. The electron remains in the excited…

Q: Consider an atom with two closely spaced excited states A and B. If the atom jumps to ground state…

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Q: Calculate the de-Broglie wavelength of the electron orbitting in the n = 2 state of hydrogen atom.

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Q: Q.2: Calculate the shortest wavelength for electron revolving in the fourth excited germanium atom,…

A: Given,  q=4.8×10-19CEnergy of germanium atom,En=-13.6n2z2  evz=Qe=4.8×10-19 C1.6×10-19 C=3for 4th…

Q: Q: The speed with which the electron must move in units (1/ms) in order to have a wavelength of…

A: The electron being a particle, also exhibits wave nature, and thus has some particular wavelength…

Q: What is the kinetic energy of an electron (in eV), if its de Broiglie wavelength is 8.08 Å? Answer:

A: Given: The de Broglie wavelength is 8.08 Ao.

Q: Singly ionized helium has a single orbiting electron, so the mathematicsof the Bohr hydrogen atom…

A: The energy levels of the singly ionized helium are specified by; En=1n2K2e22aBEn=4EnH…

Q: hydrogen atom has its electron in the n = 3 level. The radius of the electron's orbit in the Bohr…

A: Mass of electron m = 9.1×10-31 kg Radius r = 0.476 nm = 0.476 × 10-9 m

Q: Find an expression, in termsof n and the fundamental constants, for the de Broglie wavelength of an…

A: Let vn denote the speed of the electron in the orbit having principal quantum number n, e denote the…

Q: : The de Broglie wavelength of an electron in the ground state of the hydrogen atom is (a) 2πr (b)…

A: To find-De-Broglie wavelength (λ)=?Given-Hydrogen atom is in ground state

Q: The wavelengths of the Lyman series for hydrogen are given by (a) Calculate the wavelengths of the…

A: The Rydberg constant  RH=1.0973732×107 m-1

Q: So Determine the distance between the electron and proton in an atom if the potential energy ?U of…

A: Given, Potential energy of electron proton in an atom, U = 15.4 eV 1 eV = 1.6×10-19 C

Q: Calculate the shortest wavelength that can be emitted by the Li++ ion.

A: According to Bohr's theory when an electron jumps from higher orbit to lower orbit then the…

Q: (a) Using the Pauli exclusion principle and the rules relating the allowed values of the quantum…

A: a : Here we need to prove that the maximum number of electrons in a subshell is 2n2 :As we know…

Q: A positronium atom consists of a positron and an electron. In a Bohr-like model, the two particles…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: (a) How much energy is required to cause an electron in hydrogen to move from the n = 2 state to the…

A: Given Data The initial state of the electron is n1 = 2. The final state of the electron is n2 = 5.…

Q: Compute the oscillation frequency of the electron and t expected absorption or emission wavelength…

A: The force acting on an electron in Thomson's model of an atom is the electric force. Thus we have…

Q: t = 0 the hydrogen atom in the {|r}} representation is given as (0)) = ao (2x + iy) p2 [ª(21 -1₁- +…

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Q: (a) What is the minimum value of 1 for a subshell that has11 electrons in it?(b) If this subshell is…

A: The expression for the number of electrons relating to the angular momentum quantum number is The…

Q: Consider a gas discharge tube (like the one used to discover cathode rays) where low-density…

A: The Rydberg's formula which relates the wavelength of photon to electronic transition is,…

Q: A proton is fired from very far away towards a nucleus with charge Q = 120 e, where e is the…

A: When a proton is launched into a nucleus with a charge of Q=120 e, where e is the electronic charge,…