An electron in a hydrogen atom orbits the proton at a radius of 5.29 x 10-11...

An electron in a hydrogen atom orbits the proton at a radius of 5.29 x 10^-11 m. Considering the proton to be at the origin, and answering to 2 decimal places:

(a) What is the electric field due to the proton at the position of the electron? (answer in terms of r, theta, and phi).

(b) What is the resultant force on the electron? (answer in terms of r, theta, and phi).

(d) If the electron in the hydrogen atom is in a bound state, and is therefore undergoing circular motion where the Coulomb force holding it in the atom is equal to the central force of circular motion, what is the electron velocity as it orbits the atom?

Solutions

Expert Solution

We consider the proton to be a point mass and it is situated at the origin.

Now the radius of the electron orbital is

Now the charge of the proton and the charge of a electron is

a) So the electric field due to proton at the position of electron is:

b) The resultant force on the electron is:

c) Let be the mass of the electron and be its accelaration.So,

d) This same force F is responsible for the circular centripetal motion of the electron.Let be the electron velocity as it orbits the atom.

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

In one model of the hydrogen atom, an electron orbits a proton in a circle of...

In one model of the hydrogen atom, an electron orbits a proton in a circle of radius 5.28×10-11 m with a speed of 2.18×106 m/s. What is the acceleration of the electron in this model? What is the period of the motion?

In a hydrogen atom, a proton is separated from an electron by an average distance of...

In a hydrogen atom, a proton is separated from an electron by an average distance of about 5.3 10-11 meters. Use the information below to calculate the force of attraction by the electron on the proton. Electron Mass = 9.11 10-31 kg Proton Mass = 1.67 10-27 kg Elementary Charge = 1.602 10-19 C Coulomb's Constant (k) = 8.99 109 Nmm/CC Avagadro's Number = 6.02 1023 atoms/mole

A standard hydrogen atom consists of one proton and one electron. The net electric charge of the hydrogen atom is equal to

A standard hydrogen atom consists of one proton and one electron. The net electric charge of the hydrogen atom is equal toGroup of answer choices1.6 x 10-19 C.3.2 x 10-19 C.4.8 x 10-19 C.6.4 x 10-19 C.zero.

Early 20th-century physicist Niels Bohr modeled the hydrogen atom as an electron orbiting a proton in...

Early 20th-century physicist Niels Bohr modeled the hydrogen atom as an electron orbiting a proton in one or another well-defined circular orbit. When the electron followed its smallest possible orbit, the atom was said to be in its ground state. (a) When the hydrogen atom is in its ground state, what orbital speed (in m/s) does the Bohr model predict for the electron? m/s (b) When the hydrogen atom is in its ground state, what kinetic energy (in eV) does...

Determine the radius at which a 2s electron in a hydrogen-like atom of atomic number Z...

Determine the radius at which a 2s electron in a hydrogen-like atom of atomic number Z is more likely to be found? The answer is r = 5.24(a0/z) OR r = 5.24(a/z) with no units provided, but they should be there.

Consider an electron in a hydrogen atom in the n=2,l=0 state. At what radius ( in...

Consider an electron in a hydrogen atom in the n=2,l=0 state. At what radius ( in units of a0) is the electron most likely to be found?

Consider a molecule of hydrogen chloride, HCl. In this molecule, the light hydrogen atom orbits the...

Consider a molecule of hydrogen chloride, HCl. In this molecule, the light hydrogen atom orbits the heavy Cl atom, much like an electron orbits a heavy nucleus in an atom. The energy of H in the molecule is quantized. When exposed to electromagnetic field, the molecule HCl absorbs photons that promote the hydrogen atom to higher energy states, corresponding to faster rotation of H about Cl. What do you think is the approximate frequency of these photons? a) The frequency...

An electron, with a mass of 9.11×10−28 g is orbiting the nucleus of a hydrogen atom....

An electron, with a mass of 9.11×10−28 g is orbiting the nucleus of a hydrogen atom. A measurement determines the position of the electron to within ±1.63 nm. The velocity of the electron is measured as 6.39×106 m/s. What is the uncertainty in the velocity of the electron?

Suppose the electron in a hydrogen atom is modeled as an electron in a one-dimensional box...

Suppose the electron in a hydrogen atom is modeled as an electron in a one-dimensional box of length equal to the Bohr diameter, 2a0. What would be the ground-state energy of this "atom"? ______________eV

The hydrogen atom electron is in the ground state. The electron absorbs energy and makes a...

The hydrogen atom electron is in the ground state. The electron absorbs energy and makes a transition to the n=3 state. Then it returns to the ground state by emitting two photons when going to n=2 and then n=1 states. A. What are the wavelengths of these photons? B. What will be the wavelength if only one photon is emitted? C. What is the maximum number of electrons with ml=3 in the shell with n=5? D. How many electrons with...

Subjects