Please help me on this 4 part assignment. Thanks! You wish to find the size of a

Question

Please help me on this 4 part assignment. Thanks!

You wish to find the size of a single photon by using a combination of classical and quantum mechanical ideas. Consider the Bohr model of the hydrogen atom where an electron is in classical orbits like a planet. Transition: Find the energy in joules of a photon emitted as it falls from the n = 3 level to the n = 2 level. Find the frequency of the photon. Orbit: Assume that the radiation is caused by an electron orbiting in an atom with this frequency. Find the time it takes the electron to orbit once. Call the radius of the orbit r. Find the speed of the electron in terms of r. If the electron is orbiting in a circular orbit, we know the centripetal force is the Coulomb force between the proton and the electron. Thus: mv^2/r = k_e e^2/r^2 Use this relationship to find r. Now that we know r, use the expression for the centripetal force to find the acceleration a of the electron in its orbit. Fields: We wish to find the electric and magnetic fields at a point R =1.00 m from the atom in the plane of the atom's orbit. The electric field in the radiation will vary sinusoidal with the maximum electric field given by the expression: E_max = k_e ea/c^2 R where c is the speed of light. Find the maximum electric field at R. Find the maximum magnetic field at R. Find the energy density (energy per unit volume) of the electric field at R. Use the equation for the energy density: u_elementof = 1/2 elementof_0 E^2 _rms Find the energy density of the magnetic field at R. Use the equation for the energy density: u_s = 1/2 mu_0 B^2 _rms Photon size: Find the volume of the photon. You know the total energy density is the sum of the electric and magnetic energy densities. You also know the energy of the photon. Assume the energy density is uniform. Consider the photon to be spherical. Recall that the volume of a sphere is V = 4/3 pi R^3. Find the effective radius of the photon.

Explanation / Answer

Solution :-

1) The energy in joules of a photon emitted as it falls from n = 3 level to n = 2 level

We know that when energy is smaller than the wavelength is longer. Further to this, we know that the photon actually have a very less energy for the n=3 to n=2 transition.

Therefore let us assume the case of a hydrogen atom, with Z = 1 then the energy in joules of a photon emitted as it falls from nf = 3 level to ni = 2 level can be calculated as follows:-

E = (13.6 eV) [1/nf2 - 1/ni2]

E = (13.6 eV) [1/32 - 1/22]

E = (13.6 eV) [1/9 - 1/4]

E = (13.6 eV) [4-9/36]

By ignoring negative sign

E = 13.6 (5/36) = 1.89 eV = 1.89 * 1.6 * 10^-19 = 3* 10^-19 J

b) We know that E =hf

Hence frequency f = E / h =  3* 10^-19 /6.63 x 10-34 = 0.45 *10^15 Hz

Note:- There are four different questions each having various parts. As per rules I have done 1st answer with both parts.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---