Question

Consider the Schrodinger equation and its solution for the hydrogen atom. a) Write an equation that...

Consider the Schrodinger equation and its solution for the hydrogen atom.

a) Write an equation that would allow you to calculate, from the wavefunction, the radius of a sphere around the hydrogen nucleus within which there is a 90% probability of finding the electron. What is the radius of the same sphere if I want a 100% probability of finding the electron?

b) Calculate the shortest wavelength (in nm) for an electronic transition. In what region of the spectrum is it found?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
This problem deals with the probabilistic interpretation of the hydrogen wavefunction. a. Calculate the probability that...
This problem deals with the probabilistic interpretation of the hydrogen wavefunction. a. Calculate the probability that a hydrogen 1s electron will be found within a distance of 2a0 from the nucleus. b. Calculate the radius of the sphere that encloses a 50% probability of finding a hydrogen 1s electron. c. Calculate the radius of the sphere that encloses a 90% probability of finding a hydrogen 1s electron.
Based on the solutions to the Schrödinger equation for the ground state of the hydrogen atom,...
Based on the solutions to the Schrödinger equation for the ground state of the hydrogen atom, what is the probability of finding the electron within (inside) a radial distance of 3.5a0 (3.5 times the Bohr radius) of the nucleus? Express the probability as a decimal (for example, 50% would be expressed as 0.50).
Consider the electronic transition from n = 4 to n = 1 in a hydrogen atom,...
Consider the electronic transition from n = 4 to n = 1 in a hydrogen atom, and select the correct statement below: A photon of 97 nm wavelength and 2.05x10-18 J energy was emitted from the hydrogen atom in this electronic transition. A photon of 97 nm wavelength and 2.05x10-18 J energy was absorbed by the hydrogen atom in this electronic transition. A photon of 122 nm wavelength and 1.64x10-18 J energy was emitted from the hydrogen atom in this...
An electron in a hydrogen atom relaxes to the ground state while emitting a 93.8 nm...
An electron in a hydrogen atom relaxes to the ground state while emitting a 93.8 nm photon. a. Is this light visible? In what region of the electromagnetic spectrum does it lie? b. What was the initial principal quantum number, ni, of the electron undergoing the transition?
The ”most-probable” distance from the nucleus to observe the electron in a 1H hydrogen atom in...
The ”most-probable” distance from the nucleus to observe the electron in a 1H hydrogen atom in its ground state is the Bohr radius, a0= 5.29×10^−11m. What is the probability of observing the electron in a ground state hydrogen atom somewhere within any greater distance r from the nucleus a0 ≤ r <∞?
An electron in a hydrogen-like atom in the n = 3 orbital has a de Broglie...
An electron in a hydrogen-like atom in the n = 3 orbital has a de Broglie wavelength of 1.89x10-10 m. Calculate the orbit radius of the electron, in nm.
The hydrogen atom, changing from its first excited state to its lowest energy state, emits light...
The hydrogen atom, changing from its first excited state to its lowest energy state, emits light with a wavelength of 122 nm. That is in the far ultraviolet. The sodium atom, which like hydrogen has one electron that gets excited outside a core of 10 other electrons, emits light at 589 nm making a similar transition from its first excited state to its lowest state. Which of these statements would be true about the sodium and hydrogen atoms and their...
An electron in a hydrogen atom undergoes a transition from the n = 6 level to...
An electron in a hydrogen atom undergoes a transition from the n = 6 level to some lower energy level. In doing so, energy is released in the form of light. a) Calculate the frequency in s-1 (to 3 significant figures) of a photon of light associated with the highest frequency transition (i.e. largest difference in frequency) possible from the n = 6 to a lower level. (HINT: Try drawing a picture first…) b) Calculate the wavelength (in nm) of...
1. Atomic orbitals are a mathematical representation of the _____________ an electron in the region around...
1. Atomic orbitals are a mathematical representation of the _____________ an electron in the region around the nucleus of an atom. a. spin of b. frequency of c. probability of finding d. wavelength of 2. The greater the principle quantum number of an electron in a hydrogen atom, the greater the ___________ of the atom. a. potential energy b. wavelength c. speed d. frequency 3.The principle quantum number for an electron about an atom is designated by ___________ a. a...
A hydrogen atom is in its first excited state (n = 2). Using Bohr's atomic model,...
A hydrogen atom is in its first excited state (n = 2). Using Bohr's atomic model, calculate the following. (a) the radius of the electron's orbit (in nm) nm (b) the potential energy (in eV) of the electron eV (c) the total energy (in eV) of the electron eV