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course Phy 202
8/3 at 9:00*Please return by 8/4 wednesday at 6pm*
Problem Number 1
Two identical hypothetical nuclei, each with mass ( 13 - .007) amu, fuse to form a nucleus with mass ( 25 - .0069) amu and a neutron, whose mass is about 1.000867 amu. How much energy would be given off if .71 kg of these nuclei fused?
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.Mass change: 0.71kg x 1.66x10^-27(1.000867 amu) = 0.71
Energy= 1.17x10^-27(3x10^8)^2= 1.06x10^-10 J
Energy released= 6.02x10^23 x 1.06x10^-10= 6.38x10^13 J
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Problem Number 2
If in an atomic explosion a sample of .003% of the total 11 kg of fissionable material is converted to energy, how much energy is released?
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.0.003x11 kg= 0.33 kg (Change in mass?)
0.33x1.66x10^-27
=5.48x10^-29 x (3x10^8)^2
=4.93x10^-12
Released= 6.02x10^23 x 4.93x10^-12
= 2.97x10^12 J
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Problem Number 3
A beam of protons, each with rest mass about 1.6 * 10^-27 kg, are accelerated to near-light-speed velocities before entering a magnetic field of 1.7 Tesla. The magnetic field is directed perpendicular to the direction of the beam. Without taking account of the relativistic effect on mass, what should be the radius of curvature the protons if they are moving at 2.94 * 10^8 m/s as the beam passes through the magnetic field?
• What should be the radius of curvature of the beam if we take relativistic effects into account?
• What will happen to the radius of curvature as the velocities of the protons approach the speed of light?
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.B=F/qv
1.7/1.6x10^-19x2.94x10^8
=3.6x10^10 ??
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F = q v B is correct. However you are given the magnetic field and need to find the force.
The centripetal acceleration comes from this force, so F = m v^2 / r. You are given v, you can find the force and you know the mass of a proton. So you can solve for r.
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Problem Number 4
The intensity of 573 nm light falling on a photoelectric metal is 130 watts / m^2 (maximum sunlight intensity at the surface of the Earth is on the order of 1000 watts/m^2). How many photons fall on a 1 cm^2 area in a second? What is the approximate average spacing of the photons that fall on this area in a second?
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.I am really at a loss on this one. I’m trying to find an equation with intensity and wavelength in the book on light, but there doesn’t seem to be one in that section.
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You know the intensity, which is energy per second, per unit of area, and you know the area. So you can find the energy per second.
You know the wavelength and you know that E = h f, where E is the energy of a photon, h is Planck's constant and f is its frequency.
You are given the wavelength and you know the speed of light, so you can find the frequency, from which you can find the photon energy.
Having found the energy per second, you can find the number of photons per second.
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Problem Number 5
Find the velocity an electron in a circular orbit would require at a distance of 3.257 Angstroms from a proton. Find the deBroglie wavelength of this electron. Determine whether the corresponding probability wave would 'fit' the circumference of the orbit without undergoing destructive interference. [ The mass of an electron is 9.11 * 10^-31 kg; the proton has a much greater mass; Planck's Constant is 6.62 * 10^-34 J s; k = 9 * 10^9 N m^2 / C^2 ]
Lambda=h/mv.
V= h/lambdam
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.So, we have one constant, and two variables to solve for. Which should I go for first? Is there a different equation to find lambda or velocity?
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By setting centripetal force on the electron equal to its Coulomb attraction to the proton you can figure out its velocity.
From its velocity you can figure out is momentum.
Its deBroglie wavelength is equal to Planck's constant divided by its momentum (lambda = h / (m v) ).
This can be compared with the circumference of the circular orbit.
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Problem Number 6
A certain hypothetical atom contains 99 protons and 142 neutrons in its nucleus and has an atomic mass of 239.4 atomic mass units, or amu (an amu is approximately 1.66 * 10^-27 kg). How many protons and how many neutrons will it end up with if it undergoes an alpha decay? How many if it undergoes a beta decay? How many if it undergoes a gamma decay?
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.All I can find in the book is an equation that doesn’t have any meaning to this problem. The book is going from one element to another, and I am not sure what equation (if there is one) to use.
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You shouldn't be trying to learn to solve these equations from the book. Introductory Problem Set 7 is much more specific, requiring much less information than the text.
Alpha decay takes away an alpha particle, which contains 2 neutrons and 2 protons.
Beta decay emits an electron, and a neutron changes to a proton.
Gamma decay doesn't affect the number of protons or neutrons.
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Problem Number 7
What is the approximate uncertainty in the velocity of a proton known to remain within a nucleus of diameter 3.2 * 10^-15 m? What kinetic energy would the proton (mass approximately 1.6 * 10^-27 kg) have at this velocity?
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.dx=(h/2pi)/dpa
I seem to be missing the mass, so how exactly do I go about finding it? How do I go about finding the change in p (which p=mv)?
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The table that prints out with the text includes proton mass.
The uncertainty in position is equal to the radius of the nucleus.
The product of the uncertainty in position and the uncertainty in momentum is about equal to Planck's constant (also given in the table).
So you can find the uncertainty in momentum, if you know the uncertainty in position. This allows you to find the uncertainty in momentum.
If you assume that the proton has this momentum, then knowing its mass you can find its velocity.
From its mass and velocity you can find its kinetic energy.
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Problem Number 8
What is the deBroglie wavelength of an electron moving at 7.2 * 10^6 m/s?
Lambda=h/mv
=6.62x10^-34/(7.2x10^-6 x 9.1x10^-31)
=101
Should be =6.62x10^-34/(7.2x10^6 x 9.1x10^-31), which is about 10^-10 m.
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