1.A spherical bowl(R = 20 cm) contains water(n = 1.33) and your pet gold fish who, is swimming 15 cm from the centre of the bowl. You however are 35.0 cm from the edge of

the bowl-outside, of course. Describe the image your fish sees.

2.The hydrogen atom consists of a proton with an electron in orbit about the proton. The laws of quantum mechanics determine that the radius of this orbit is 5.29x10^-11 meters. Therefore, calculate
a) The electric potential the electron experiences.
b) The next available orbit has a radius four(4) times that of the orbit described above
c) When an electron goes from the higher energy orbit to lower energy orbit, it releases the change in energy as photon. What is the wavelength of the emitted photon.

1. Use the formula for refraction at a spherical surface, where the index of refraction changes from 1.33 to 1.

The formula can be found at
http://www.physnet.org/modules/pdf_modules/m222.pdf

1. To describe the image that the fish sees, we need to consider the principles of refraction. When light passes from one medium to another, it changes direction, and this bending of light is called refraction.

In this case, the fish is swimming 15 cm from the center of the bowl, and you are 35 cm from the edge of the bowl. The light rays coming from the fish will travel through water and then pass through the curved surface of the bowl before reaching your eyes outside the bowl.

Since the bowl is spherical, the surface of the water acts as a lens, and the light rays will converge or diverge as they pass through it. The fish will perceive the outside world as if it were located on a curved surface due to the refraction of light. The exact image the fish sees will depend on the position and properties of objects outside the bowl.

To visualize the image, you can imagine drawing lines from the fish's position to different points outside the bowl and trace those lines backward through the bowl's curved surface. The final image will appear distorted and magnified due to the refraction of light at the water-air interface.

2. a) To calculate the electric potential the electron experiences in the hydrogen atom, we need to use the formula for electric potential energy:

Electric Potential (V) = k * (q / r)

Where:
- k is the Coulomb's constant, approximately 9 × 10^9 Nm^2/C^2.
- q is the charge of the proton (which is equal to the charge of the electron but with opposite sign), approximately -1.60 × 10^-19 C.
- r is the radius of the orbit.

Substituting these values into the formula, we get:

V = (9 × 10^9 Nm^2/C^2) * (-1.60 × 10^-19 C) / (5.29 × 10^-11 m)

Calculate the expression to find the electric potential the electron experiences.

b) If the next available orbit has a radius four times that of the orbit described above, we can calculate the new radius using the given information.

New radius = 4 * (5.29 × 10^-11 m)

c) When an electron transitions from a higher energy orbit to a lower energy orbit, it releases the change in energy as a photon. The energy difference between the two orbits can be determined using the formula:

ΔE = -13.6 eV * (1/n_final^2 - 1/n_initial^2)

Where:
- ΔE is the change in energy.
- -13.6 eV is the energy of the electron in the hydrogen atom at the first energy level (n = 1).
- n_final is the final energy level.
- n_initial is the initial energy level.

Once you have calculated the change in energy, you can use the equation:

E = hc/λ

Where:
- E is the energy of the photon.
- h is Planck's constant, approximately 6.63 × 10^-34 J·s.
- c is the speed of light, approximately 3.00 × 10^8 m/s.
- λ is the wavelength of the emitted photon.

Substitute the change in energy into the second equation to find the wavelength of the emitted photon.