Waves and Atoms (Homework 3-380)

1. Waves show the phenomena of reflection, diffraction, refraction, interference, and absorption. Associate at least one or two of these with each of the following. (20%)

You see a mirage. refraction

You hear someone whispering just around the corner in the next room. diffraction

You see a rainbow in the sky. Interference and diffraction

The sunset is red. refraction

You hear beats when two guitar strings are plucked simultaneously.interference

You hear an echo. reflection

You see yourself in a mirror reflection

2. The sun emits $3×10^{32} J$ of energy every day. Assume it emits only yellow light (wavelength of $6*10^{-7}m$). (15%)

What is the energy of each photon of yellow light?

Energy = Planck constant* frequency = Plank constant*light speed/wavelength=

$=6,626*10^{-34}*3*10^8/6*10^{-7} =3,3*10^{-19} J$

How many photons does the sun emit every day?

Photon number = total energy/photon energy $=3*10^{32}/3,3*10^{-19} =9*10^{50}$ photons

3. What were 3 examples of problems in physics at the turn of the 20th century (around 1900) that led to the development of quantum mechanics? (20%)

Problem 1. The model of the atom ( see model of Bohr)

Problem 2. External photoelectric effect (see Einstein model of photoelectric effect)

Problem 3. The crystalline bond (see the model of the covalent bond in chemistry)

4. Where was the uranium found in the Earth produced? (10%)

The uranium found in the Earth mines was produced in the explosion of the supernovas stars. All the chemical elements transcending Fe are produced in such explosions.

5. Einstein stated that $E = m c^2$. Assume a person has a mass of 60 kg, and somehow all of this mass is converted to energy. (20%)

How much energy (in joules) would be released?

$E =m*c^2 =60*(3*10^8)^2 =5.4*10^{18}$ J

If this energy were released over a years time, what would be the average power released (in watts)?

$P = E/Time =5.4*10^{18}/365/24/60/60 =1.71*10^{11}$ W

How many power plants is this equal to in output?

A nuclear plant has a capacity of around $4 GW = 4*10^9 W$ the number of nuclear plants is

$No =1,71*10^{11}/4*10^9 =42.8$ nuclear plants

6. The atom is mostly empty. If all the atoms in the Earth collapsed in to the size of a nucleus, what would be the Earth’s diameter? (15%)

The diameter of an atom nucleus is around $10^{-15}$ m. The diameter of an atom is around $10^{-10}$ m

The ratio atom nucleus /atom diameter $= 10^{-5}$.

The Earth normal diameter is $6400*2 =12800 Km$

The new diameter will be $12800*10^{-5} =0.128 Km =128 m$