An electron from a Ti ^ + 2 hydrogen ion leaps from one orbit with radius 13.25 angstrom to another orbit with radius 2.12 angstrom. determine the energy (Joule) e produced in said transition and the wavelength (in cm)

    E  = 0.2276 10⁻¹⁹ J ,  λ = 8.73374 10⁻⁴ cm

Explanation:

Bohr's atomic model can be used for hydrogen-type atoms, that is, they have a single electron in their last orbit, this is the case of doubly ionized Titanium.

It is much easier to work in EV units.

          r = a₀ / Z n²

          E = - 13.606 (Z² / n²)

where ao is the Bohr radius, which is the ground state orbital of hydrogen a₀ = 0.0529 nm, Z is the atomic number of titanium, and n is an integer that represents the different states of the system.

a) Let's look for the energy, for this we look for the integer numbers of these orbits

r = 13.25 A = 1.325 nm

          r = a₀ / Z   n²

         n = √(Z r / a₀)

the atomic number of titanium is Z = 22

         n = √ (22  1.325 / 0.0529)

         n = 23

r = 2.12 A = 0.212 nm

         n = √ (22  0.212 / 0.0529)

         n = 9

now we can calculate the energy of the transition

         E = 13.606 (1 / - 1 / )

         E = 13.606 (1/9² - 1/23²)

         E = 13.6060 (0.010455)

         E = 0.1423 eV

Let's reduce to J

         E = 0.1423 eV (1.6 10⁻¹⁹ J / 1eV) = 0.2276 10⁻¹⁹ J

To find the wavelength of the transition, use the Planck relation

         E = h f

the relationship of frequency and speed of light

         c = λ f

  we substitute

         E = h c /λ

         λ = hc / E

        λ = 6.626 10⁻³⁴ 3 10⁸ / 0.2276 10⁻¹⁹

        λ = 8.73374 10⁻⁶ m

       λ = 8.73374 10⁻⁴ cm

it is very well related to a lot of things but with my limited knowledge i can confidently say that the answer is space.

the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees.