The Bohr radius (a0) is a physical constant, equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state (non-relativistic and with an infinitely heavy proton). It is named after Niels Bohr, due to its role in the Bohr model of an atom. Its value is 5.29177210903(80)×10−11 m.
Soo. I think this problem is too direct and easy so I think I got it in wrong way: p=h/r and then plug in the K and V and then we get E=E(r) and get derivative and we have minimum? What do you think? is there sth I am missing?
When I looked up for Bohr radius, the formula has ##q## in it, which is charge of the object. For this question, the electron and proton are replaced by sun and Earth so it means that I have to know the charge of Earth and sun?
Thanks
What is the exciton Bohr radius? I understand that the exciton is the paired distance of an electron and hole. How does the Bohr radius play a role in this?
Homework Statement
On which orbit of hydrogen atom an electron has the speed of 734 km/s?
Homework Equations
Bohr's second postulate: mvr=nh,m=9.109\cdot 10^{-31}kg,v=734 km/s,h=6.626\cdot 10^{-34} m^{2}kg/s
The Attempt at a Solution
By using the second Bohr's postulate, we get 6686.006\cdot...
I'm doing a homework problem where it asks to calculate the diameter of a hydrogen atom with n=600. I used the equation $$r=\frac{n^2a_0}{Z}$$ where $$a_0=0.529e^{-10}m$$.
Solving for r yields:
$$r=\frac{(600^2)(0.529e^{-10}m)}{1}=1.90e^{-5}m$$
Multiplying by 2 to get the diameter yields...
Homework Statement
Positronium is a hydrogen-like atom consisting of a proton and an electron revolving around each other. Find the allowed radii and energies of the system.
Homework Equations
See solution attempt.
The Attempt at a Solution
The allowed radii of the positron/electron system...
Homework Statement
A muon is a particle with a charge equal to that of an electron and a mass equal to 207 times the mass of an electron. What is the radius and energy of the ground state of hydrogen if the electron is replaced with a muon? Don't forget to use the concept of reduced mass...
I figure that at large enough distances, the potential field of an ion is just the Coulomb potential for its net charge. But what happens at scales comparable to the ion's Bohr radius? Could there be, for example, some sort of screening effect from the electron shell that changes the potential...
Homework Statement
Both Newton's gravitational law and Coulomb's law are inverse-square laws: The force of attraction
between the sun (S) and Earth(E) has (G*m_S*m_E)/r^2, whereas the force of attraction between an electron and a proton in a hydrogen atom is (e^2)/(4*pi*epsilon_0*r^2). Derive...
Homework Statement
Using the Bohr model, find the atomic radius for a singly ionized He+ atom in the n =
1 (ground) state and the n = 2 (first excited) state. Then find the wavelength of the
emitted photon when an electron transitions from the n = 2 to the n = 1 state.Homework Equations
a_0 =...
Homework Statement
Suppose an electron was bound to a proton, as in the hydrogen atom, but by the gravitational force rather than by the electric force. What would be the radius of the first Bohr orbit?
Homework Equations
r = h^2 / 4∏^2*mke^2
The Attempt at a Solution
I'm not...
I am studying for my exam and I have run into this problem. The problem is given here http://faculty.mint.ua.edu/~pleclair/PH253/Homework/Spring_2010/HW6-7_atoms_12Mar10/HW6-7_atoms_12Mar10_SOLN.pdf"],[/PLAIN] it is #9.
I don't understand why -e ≠ ∫ρdV from 0 to the bohr radius, a0. If all...
from wikipedia - "The Bohr radius is a physical constant, approximately equal to the most probable distance between the proton and electron in a hydrogen atom in its ground state."
in Planck units bohr radius (a0) = (mp/me).(1/\alpha).(lp)
the 1st 2 terms of the RHS of the equation are...
Homework Statement
the equation for the bohr radius is
4pi (permitivity of free space) * (reduced Planck constant)/
(elementrary charge)2(mass of an electron)
The Attempt at a Solution
let's just just focus on orders of magnitude:
(10^-12 * 10^-34)/(((10^-19)^2)*(10^-31)...
[SIZE="3"]Homework Statement
Determine an expression for the Bohr radius (a_{0} from the following approximation. The electron moves to the nucleus to lower its potential energy,
V(r) = -\frac{e^{2}}{r}
If the electron is in domain 0\leqr\leq\bar{r}, then we may write...
Creating metallic hydrogen has proved more difficult than expected. One explanation would be that the Bohr radius of Hydrogen is smaller than expected. Is there any other evidence of an error in Bohr radius predictions?
Homework Statement
Given the potential energy V(r)=-\frac{1}{4\pi \epsilon_0}\frac{e^2}{r} (where e is the unit charge), use the uncertainty principle \Delta x \Delta p \geq \hbar to find the Bohr radius r_B for a hydrogen atom and the ground state energy E_0.
Hint: write down the kinetic...
Homework Statement
If the attractive forces between an electron and proton only due to gravity is
F=(Gx Me x Mp)/r^2.
What is the lowest gravitational Bohr radius?
c=2.99799 x 10^8 m/s
Me= 9.10939 x 10^-31
Mp=1.67262 x 10^-27
h= 1.05457 x 10^-34
G= 6.67259 x 10^-11 Nm^2/kg^2...
Some places say (including this paper) claim the bohr radius of muonic hydrogen is 285http://ethesis.unifr.ch/theses/downloads.php?file=LudhovaL.pdf
Many more peer reviewed papers say it is 256 fm, or 255 fm though. (search for '256 fm muonic' in teh googlez).
So who is right? And more...
Thanks in advance for anybody who is kind enough to help me. No this isn't for my homework. I am not even enrolled in school. I am doing some calculations for personal research.
But I need to know the ground state radius of a muonic hydrogen atom to help prove my theory.
I already know the...
while doing some calculations such as calculating the Bohr radius or velocity of an excitons in semiconductors such as GaAs I didnt understand why is it allowed to use the static permittivity even though the electron and hole aren't as heavy and the spectra is measured at high frequencies such...
Homework Statement
Consider an hydrogen atom in its ground state, what is the probability that the electron is found inside the Bohr Radius?
Homework Equations
The probability of finding the electron at bohr radius is maximum. but the probability over the range from 0 to bohr radius...
Homework Statement
i have been given a question that asks to me to calculate the radii of the first, second and third 'permitted' electron orbits in hydrogen. I did this fine by using the Bohr Equation, each time just changing the n value to either 2 or 3 resulting in the first value of the...
an electron is distributed around a proton according to the volume charge density \rho = A e^{-2r/a_o} where A is a constant, a_o is the Bohr radius and r is the distance from the center of the atom.
Find A:
we know that Q=\int \rho dV = -e
i was wonder if this was the integral that i set up...
for ions with more than one proton ie. He+, Li2+ and Be3+, doesn't the extra charge factor into the equation? because it seems only the elementary charge is http://en.wikipedia.org/wiki/Bohr_radius" , hence rendering it independent of amount of positive charge present.